It is somewhat accurate, but not that much. In short - non-German but not Jewish (Yiddish or Hebrew) names were not forbidden in any way but since 1938 officials had the power to reject foreign names when no justification for that choice was provided. Additionally, naming children with specified Jewish names was forbidden for non-Jews but required for Jewish population.
There were rules related to the naming of children, abut they were guidelines describing 'desirable names' rather than 'list of banned names', with an exception for distinctive Semitic names rarely used outside Jewish communities. This 'Germanic' notion stemmed from the national sentiments following restitution of German Empire in 1871 and was heavily strengthened in the Third Reich due to its totalitarian character allowing political agenda to permeate all facets of social life. The Disney movie shows a list that includes mostly typical Jewish names (technically, Biblical ones) in its English spelling with 'Winston' (Churchill) and 'Franklin' (Roosevelt) prominently displayed at the top. And although there is more than grain of truth to the former, the latter is pure fiction
In general, until 1938 there was no such things as 'banned names', as there was no a law strictly forbidding parents from choosing any name for their children, although even prior to the ascent of Hitler, outlandish names were still frowned upon, much like anywhere in Europe. In the German Empire all names of European origin were fair play, as evidenced by the highest-ranking members of Nazi Party whose names were Germanic (Henrich Himmler, Adolf Hitler, Rudolf Hess), Latin (Martin Bormann), Greek (Konstantin von Neurath, Philip Bouhler), Nordic (Hjalmar Schacht, Baldur von Schirach) or Hebrew (Joachim von Ribbentrop, Joseph Goebbels). This changed in 1938, when the the Ministry of the Interior corollary 'Richtlinien über die Führung der Vornamen' (Guidelines for giving first names) of 18 August stated that 'Non-German first names will only be allowed for children of German citizens if a acceptable reason is given (e.g. membership of non-German ethnic group, family customs or family relations'. It should be noted however, that this rule made a specific exception for Romance and Semitic names 'that due to centuries-old tradition are no longer considered foreign in popular opinion (such as Hans, Joachim, Peter, Julius, Elisabeth, Maria, Sofie, Charlotte)'. On the other hand, it excluded Nordic names 'that are unfamiliar and rarely used in Germany (e.g. Björn, Sven, Ragnhild)'. Additionally, special rules covered typical Jewish names. Since 1.1.1939 (date when the rules entered into force), Jews who were German national or stateless persons could name their children only with names listed in an annex (see bottom of this text). Conversely, non-Jews were not allowed to give their children any of such names. Furthermore, all Jews not bearing any of the listed names, had to officially adopt additional name of Israel (for men) or Sara (for Women).
'Second ordinance implementing the rules concerning the change of surnames and given names' from 17th August 1938 adds the requirement to use the 'additional Jewish names' (Israel/Sara) in all official documents, including all legal and trade documents. It also details the punishment for not complying with rules. Willful violation of the last rule was punished by imprisonment up to six months, or to one month if it was considered to be a result of negligence rather than a deliberate obfuscation. Jews who did not comply with the requirement to adopt the additional name (i.e. did not registered it with the their local registrar office within specified time period) were liable to fine or an imprisonment up to one month.
As stated above, Nordic names were not considered 'proper German names'. This most likely created at least a bit of contention (most likely in Schleswig-Holstein, a region neighbouring Denmark) because Director of State Registry Office (Stadesamt), Reinhold Wlochatz addressed this issue in the 10th edition of 'Auswahl gebräuchlicher Vornamen' (lit. 'Selection of usable first names') issued in 1942. He explained that: 'First names that are characteristic for northern Germanic peoples - Danes, Swedes, Norwegians and so on, cannot be considered German first names and are no more desirable than any other foreign names. There is a difference though, when it comes to the names that are used among speakers of Low German inhabiting Frisia, Jutland, Dithmarschen and so on, beacuse Low German and its numerous dialects is no less German than "High German" is' (internal quoting marks as per original).
It may be also interesting that the list of 'desirable Germanic names' presented in many popular 'family books' before 1938 was based on linguistic research, not the actual usage and thus included names that were indeed Germanic in origin although much more common outside Germany such as Ottokar (popular in Hungary) or Ulla (common in Sweden) while among 'names of foreign origin' one could find such popular German names as Anna, Eva, Angela, Grete, Maria, Hans, Johann, Max, Matthias, Michael, Martin, Georg or Klaus (this was addressed by the law as described above). The annex delineating the Jewish names is even more peculiar due to several reason. First, because of the finite form of the inventory of the Jewish names, names absent from said list were not able to be used by German Jews but could be used by non-Jews and this applies to such names as Estera, Abraham, Judit or Rut (the list misses the first one entirely, and contains only Yiddish forms of the latter, to wit 'Avrum', 'Judis' and 'Rause'). Similarly, the list includes a lot of other typically Yiddish names, very rarely used by generally urban Jewish population in Germany, but enjoyed popularity among Polish and Russian Jews, especially the inhabitants of small, predominantly Jewish towns (one theory says that the rule was written with conquest of these territories in mind, another states that it was a general harassment tactic, as in Germany, Yiddish names were considered 'rural' and 'unsophisticated' in comparison with Hebrew equivalents, not to mention 'strange' for most Germans what could further alienate German Jews from their neighbours).
I'm not sure whether it is appropriate to add such an element to the post, but in case someone is interested, I'm including full index of Jewish names considered 'ineligible' for German citizens by the document quoted above. Here it goes (spelling as per German original):
Inventory of Jewish first names
Annex to the corollary from 18th August 1938 (I d 42 X/38-5501b), published in the Journal of the Reich and Prussian Ministry of the Interior, vol. 35, 24th August 1938.
a) Male given names
Abel, Abieser, Abimelech, Abner, Absalom, Ahab, Ahasja, Ahasver, Akiba, Amon, Anschel, Aron, Asahel, Asaria, Ascher, Asriel, Assur, Athalja, Awigdor, Awrum, Bachja, Barak, Baruch, Benaja, Berek, Berl, Boas, Bud, Chaggai, Chai, Chajin, Chamor, Chananja, Chanoch, Chaskel, Chawa, Chiel, Dan, Denny, Efim, Efraim, Ehud, Eisig, Eli, Elias, Elihu, Eliser, Eljakim, Elkan, Enoch, Esau, Esra, Ezechiel, Faleg, Feibisch, Feirel, Feitel, Feiwel, Feleg, Gad, Gdaleo, Gedalja, Gerson, Gideon, Habakuk, Hagai, Hemor, Henoch, Herodes, Hesekiel, Hillel, Hiob, Hosea, Isaac, Isai, Isachar, Isboseth, Isidor, Ismael, Israel, Itzig, Jachiel, Jasse, Jakar, Jakusiel, Jecheskel, Jechiel, Jehu, Jehuda, Jehusiel, Jeremia, Jerobeam, Jesaja, Jethro, Jistach, Jizack, Joab, Jochanan, Joel, Jomteb, Jona, Jonathan, Josia, Juda, Kainan, Kaiphas, Kaleb, Korach, Laban, Lazarus, Leew, Leiser, Levi, Lewek, Lot, Lupu, Machol, Maim, Malchisua, Maleachi, Manasse, Mardochai, Mechel, Menachem, Moab, Mochain, Mordeschai, Mosche, Moses, Nachschon, Nachum, Naftali, Nathan, Naum, Nazary, Nehab, Nehemia, Nissim, Noa, Nochem, Obadja, Orew, Oscher, Osias, Peisach, Pinchas, Pinkus, Rachmiel, Ruben, Sabbatai, Sacher, Sallum, Sally, Salo, Salomon, Salusch, Samaja, Sami, Samuel, Sandel, Saudik, Saul, Schalom, Schaul, Schinul, Schmul, Schneur, Schoachana, Scholem, Sebulon, Semi, Sered, Sichem, Sirach, Simson, Teit, Tewele, Uri, Uria, Uriel, Zadek, Zedekia, Zephania, Zeruja, Zewi.
b) Female given names
Abigail, Baschewa, Beile, Bela, Bescha, Bihri, Bilha, Breine, Briewe, Brocha, Chana, Chawa, Cheiche, Cheile, Chinke, Deiche, Dewaara, Driesel, Egele, Faugel, Feigle, Feile, Fradchen, Fradel, Frommet, Geilchen, Gelea, Ginendel, Gittel, Gole, Hadasse, Hale, Hannacha, Hitzel, Jachet, Jachewad, Jedidja, Jente, Jezabel, Judis, Jyske, Jyttel, Keile, Kreindel, Lana, Leie, Libsche, Libe, Liwie, Machle, Mathel, Milkele, Mindel, Nacha, Nachme, Peirche, Peßchen, Pesse, Pessel, Pirle, Rachel, Rause, Rebekka, Rechel, Reha, Reichel, Reisel, Reitzge, Reitzsche, Riwki, Sara, Scharne, Scheindel, Scheine, Schewa, Schlämche, Semche, Simche, Slowe, Sprinze, Tana, Telze, Tirze, Treibel, Zerel, Zilla, Zimle, Zine, Zipora, Zirel, Zorthel.
Erich Ehrenreich, The Nazi Ancestral Proof: Genealogy, Racial Science and the Final Solution, Indiana University Press, 2007
Uwe Dietrich Adam, Judenpolitik im Dritten Reich, Düsseldorf 2003
Richard Bessel (ed.), Life in the Third Reich, Oxford University Press, 2001