The French used to have one of the strictest naming laws in Europe, with a list of acceptable names that had to be used. However, a series of court cases (some by Breton nationalists who wanted to revive ancient Breton names that weren't on the official list) eventually led to a change in the law. Since 1993, French parents have been able to give their children any names they wish. Registrars don't have the power to refuse to register names on their own, though they can refer names they think would be detrimental to the child to a court for a ruling. However, this almost never happens.
At least until recently Denmark still had a list of names which are officially approved of. If you wanted to give a child a name which is not on the list, and both parents are Danish citizens, I believe one had to get special permission from the government. However, recently the lists of names disappeared from the official government website. I don't know if that means the law has changed and there is no longer a specific list or not. Perhaps someone from Denmark will enlighten us.
Germany and Austria have laws which prevent parents from giving children names which do not clearly designate their gender, prevent parents from turning surnames into given names, and require that parents be able to prove that any name they give has been used in the world somewhere before. Sweden also has laws which prevent turning surnames into given names, and which allow registrars to refuse to record names that they think would be detrimental to the child, though Swedish correspondents have told me that law is very seldom enforced.
There probably are other continental European countries which have or have had laws regarding naming. Japan also has laws which determine the kanji characters that may be used in creating given names.