We are expecting to have our first baby and my husband really likes the name Theodor (after Theodor Herzl) but I read it is not a Jewish name (it is Greek). Is it appropriate to name a child after a Jew when the name originates from another culture?
Many great Jewish names have non-Jewish roots.
Moshe was given a non-Jewish name by his adopted Egyptian parents. (I know plenty of people will get upset at me for making a claim based on scientific evidence and not halachic evidence, but Moshe is actually a common ancient Egyptian name - we have archaeological evidence of many people with that name).
Avraham was named by his non-Jewish parents, and since there were no Jews around at the time, it seems impossible for this to have been a Jewish name.
Shifra was trusted by Pharaoh because she has an Egyptian name.
Tzipora (Moshe's wife) was Midianite.
Hadassah tried to hide her Jewish identity by taking on the more locally acceptable name of Esther.
Yael - Technically there's a Machloket on whether or not she was Jewish, and the possibility that the name's origins are non-Jewish and that doesn't seem to bother anyone. (Seventh most popular Jewish girl's name in Israel according to JPost)
Naamah was a descendant of Cain
Many last names that we think of as stereotypically Jewish are actually just common surnames. See this article for a good rundown of where many common Jewish surnames come from. Many of them have secular origins derived from the surrounding culture.
We sometimes adopt names from local culture and if we use it long enough, it becomes Jewish in people's minds. What counts as "Jewish" name comes and goes based on the environment, language, and culture. Adolf was once a Jewish name. So was Ishmael.
In summary, name your kid whatever you want and don't worry about what other people think. B'sha'a tova.
It seems to me that the medrashim praising the Jews for their use of Jewish names should make one wonder what constitutes a Jewish name and why the use of Jewish names is praiseworthy; among the Biblical generations the concept seems less obvious than it is for us.
Perhaps a name is Jewish because it makes it's bearer recognizable as a Jew, or because it expresses a Jewish worldview (such as by praising G-d). Perhaps this is praiseworthy because of some practical consequence of these qualities: discouraging assimilation, making Jews feel the weight of our other praiseworthy (or disgraceful) behavior, or simply helping Jews find one another.
It seems to me that the name Theodor might "read" as Jewish because of Hertzl, and that a somewhat corresponding Hebrew name like Nassaniel/Nathaniel (which, like Theodor, means "G-d has given") would do so even more strongly. (Other possible references to Hertzl would include Binyomin Ze'ev, Hertzl's Hebrew name, which rosends suggested; and Hershel or Hirsh, perhaps related to Hertzl in etymology.)