I'd seen some poster that said it's horribly wrong to ever give your kid a non-Jewish/non-Hebrew name. Is that the norm?
For plenty of good Jews, their English name is the English cognate of their Hebrew name (Solomon/Shlomo, Avraham/Abraham, etc.). The letterhead of ultra-right-wing Rabbi Yoel Teitelbaum of Satmar read "Joel Teitelbaum." If someone is Solomon/Shlomo, no matter which they go by, that just goes into a Halachic document as "Shlomo"; Solomon doesn't even need to be mentioned.
Plenty of good Jews go their entire lives by a Hebrew name, but have an English (non-Biblical) name on their legal documents, for convenience. There's a very famous American rabbi "Moshe" today who's legally "Max."
Rabbi Moshe Feinstein says it's preferable, but not absolutely required, to give some sort of Jewish name. When people named their kids "Alexander" out of respect to Alexander the Great (just Alexander, no Hebrew name or anything), they overrode a preference, but not a law.
He also says that the Hebrews enslaved in Egypt needed to keep their Hebrew names, as before Judaic Law was handed down at Sinai, all they had was Hebraic culture. Once the law came around, we have that instead.
This is an old question so I doubt I'll get too many upvotes, but I figured that I should weigh in anyway considering my own name :-)
First, historical examples: on the one hand, there's a midrash (Vayikra Rabba 32) that states that the Jews merited to be saved from Egypt because they 'didn't change their name', among other cultural differences which they kept separate from the Egyptians. On the other hand, there have been many such sages in the time of the Mishnah and Gemara that have had Greek names (one Sage's father was even names 'Titus', mentioned in Yerushalmi Terumos 42a). It could be, though, that these names were 'adopted' and were actually considered "Jewish" at the time, or maybe these Sages were themselves righteous talmidiei chachamim but their parents (who named them) were not. (However, in Nedarim 81a we see that R. Yose ben Chalafta's name was Vardimos.) In addition, Sefer Daniel mentions that Daniel and his friends had Babylonian names which they used in court, but these might have been forced upon them by the Babylonian authorities or only acceptable for Jews who were forced to be in the king's palace.
It also appears to be that in Medieval times, Jews kept two names: a non-Jewish one and a Jewish one. This is evident from the Rashba quoted by the Ran on the Rif (Gittin 18a), which is quoted in the Magid Mishnah (Geirushin 3:13) as coming from the Ramban. While it's clear that the Jews of his time and place had two names, it isn't so clear if the Jews ever used their secular name among themselves, or only used it when they were interacting with non-Jews.
The Mabit (Shu"t 1:276) writes that a person should never name a child after a non-Jew or after someone who lived before the time of Avraham, because a person should only use the name of someone 'who kept the entire Torah'. Many have argued on this particular idea (for which the Mabit doesn't have a clear source), namely: the Chida (Birkei Yosef Y.D. 265:6), R. Eliezer Fleckeles (Shu"t Teshuvah Me'ahava 1:35) and the Pischei Teshuvah (also Y.D. 265:6)
The Maharam Shick (Teshuvah Y.D. 169), Maharshag (Teshuva 2:194), R. Shlomo Kluger (Shemos Anashim 142) and the Rogetchover Gaon (Teshuvah 275) all write that giving a non-Jewish name to one's child is a violation of the Biblical prohibition of following in the ways of the nations. The Maharam Shick understands this to be the opinion of Tosfos Gittin 34b who write that it would be anathema to use a non-Jewish name in a divorce document, and they cite the above-mentioned midrash as proof.
Rav Moshe Feinstein (Igros Moshe O.C. 4:66), however, didn't see fit to prohibit the practice of using secular names, as so many Sages or other Jews mentioned in the Gemara have Greek or Roman names. He says that the Jews in Egypt may have been saved for their cultural adherence to Judaism, but that was only relevant when they didn't have the Torah to keep them together - but we keep halakha, so we shouldn't worry about certain cultural things such as names.
Furthermore, R. Asher Weiss interprets the Tosfos quoted earlier differently, as referring only to Jews who have apostatized. He points out (Minchas Asher Shemos 1) that the Gemara in Gittin actually states explicitly (daf 11b) that Gittin which come from outside of Israel are kosher when non-Jewish names are used, because "רוב ישראל שבחו"ל שמותיהם כשמות עכו"מ", 'most of the Jews in the diaspora have names like those of the idolaters'. Clearly, this was common and not looked upon as a major issue (the Sages would usually note the things that diaspora Jews do incorrectly). Based on this, the Maharshdam (Teshuvah Y.D. 199) writes that despite the fact that there's a prohibition to adopt non-Jewish actions, there's no problem in adopting non-Jewish names.
At the end of the day, though, R. Asher Weiss still advises against it, mainly for mystical or kabbalistic reasons. Thus, he feels that it's better for a person not to give a child a non-Jewish name, unless it's one that has already been accepted among Jews as "culturally Jewish". (Such as Klonimus Kalman or Alexander)
In Ashkenaz (Germany-France) there was a ceremony called Chol Kreish which was for giving a baby its non-Jewish name.
So it can't be horribly wrong.
As an aside, the Jewish and secular names did not always match, with people being called (for example) Nathan as their Jewish name, and Joseph as their secular name (as was the case with my great grandfather.)
I think it is more important to give a child a name that is socially Jewish than linguistically Hebrew. For example, one of the greatest sages mentioned in the Mishna is Antignos, who clearly had a Greek name, but presumably that name was culturally Jewish.
Man great Jews had non-Jewish names, and although they didnt name themselves, they didnt hide their names. These names include: Tanach Mordechai (not a Jewish name) and Ester, probably derived from Ishtar the Babylonian equivalent of Venus. (I think there is a Yalkut Shim'oni which makes this connection). Chazal: Antignos, Avtalyon, Akiva, Somchos, Onkelos / Aquilos, and Tarfon. Rishonim: Maimon, Vidal (Magid Mishna), and Peter (Tosafist) Acharonim: Vidal (tzorfati) just to name a few.