What names are not allowed for Muslim babies?

Mostly, you can choose freely. Only a few kinds of names are not allowed: names that claim a title belonging to Allah alone, names that mean "servant of" anyone but Allah, and names of idols or false gods. Names with a bad meaning or a boastful meaning are discouraged. Everything else, in any language, is fine.

1. Names that belong to Allah alone

Some names and titles are reserved for Allah, such as Al-Khaliq (the Creator), Ar-Razzaq (the Provider) and Ar-Rahman (the Most Merciful) used by themselves. The Prophet ﷺ said that the most awful name in Allah's sight on the Day of Resurrection is a man calling himself "Malik al-Amlak", the King of Kings (Sahih al-Bukhari 6205).

Adding "Abd" (servant) fixes this: Abdul-Khaliq or Abdur-Rahman are beautiful names. Some of Allah's names are also used of people in the Quran, for instance "gracious and merciful" for the Prophet (Quran 9:128), so names like Karim or Rahim without "Al" are widely accepted. If you aren't sure about a particular name, ask your imam.

2. "Servant of" others, idols and false gods

The Prophet ﷺ said that the names dearest to Allah are Abdullah and Abd al-Rahman (Sahih Muslim 2132). By contrast, a name saying "servant of" a prophet, saint, Imam or idol, like Abd al-Nabi, Abd al-Rasul or Abd al-Masih, gives to a created being a status that belongs to Allah alone. Scholars say to avoid these.

Names that honour a pagan god or an idol, such as those worshipped before Islam, are not allowed. Scholars also advise against naming a child after Iblis (Satan) or notorious tyrants like Pharaoh. The same goes for a name that is the title of a false god in another religion.

3. Bad meanings and boastful meanings

Bad meaning: the Prophet ﷺ changed the name of 'Umar's daughter 'Asiya, meaning "disobedient", to Jamila, "beautiful" (Sahih Muslim 2139).
Self-praise: he disliked the name Barra, "pious", because it sounds as if you're praising yourself. He told Zainab, "Don't hold yourself to be pious. It is God alone who knows the people of piety among you" (Sahih Muslim 2142).

Check the meaning in Arabic and in your local language. Names can sound innocent in one language and awkward in another.

What is not a problem

Names of prophets and Companions: Muhammad, Ibrahim, Maryam, Aisha, Omar and so on are all fine.
Non-Arabic names: names with good meanings from any culture are allowed.
Family names: honouring a grandparent is fine if the meaning is acceptable.

The Prophet ﷺ said that on the Day of Resurrection you will be called by your names and your fathers' names, so give yourselves good names (Sunan Abi Dawud 4948). For ideas, see What Muslim names work well in the US and UK?

If a name is already given

If your child, or you, already has a name that falls into one of these categories, you can change it. The Prophet ﷺ did exactly this. If it's just a name you dislike, there is no obligation. See Do I have to change my name after becoming Muslim? And for the full picture of choosing a name, see How do I choose a Muslim baby name?

Key points

Avoid names reserved for Allah, like "King of Kings".
Avoid "servant of" anyone but Allah, such as Abd al-Nabi.
Avoid names of idols and false gods.
Avoid bad or boastful meanings. Everything else is open.

Tip: Before you commit, search the name together with the word "meaning" in two or three sources, and ask an imam or an Arabic-speaking friend to confirm it.