The hadeeth “The best names are those which describe one as a slave of Allaah or which are derived from the name Muhammad” is not saheeh
This hadeeth is not saheeh and it has no basis.
It says in Kashf al-Khafa (1/468): “The best names are those which describe one as a slave of Allaah or which are derived from the name Muhammad”. Al-Najm said: This is not known. It was also narrated with the wording, “The most beloved of names to Allaah are those which describe one as a slave of Allaah or which are derived from the name Muhammad”, al-Suyooti said: I could not find any source for this hadeeth. End quote.
It says in al-Maqaasid al-Hasanah (p. 87): As for what is frequently said, “The best names are those which are derived from the name Muhammad or which describe one as a slave of Allaah”, I do not know it. End quote.
Al-Albaani (may Allaah have mercy on him) said: “The best names are those which describe one as a slave of Allaah or which are derived from the name Muhammad” – there is no basis for this, as has clearly been stated by al-Suyooti and others. End quote from al-Silsilah al-Da’eefah, 1/595, no. 411
There is a saheeh hadeeth about the virtue of being a slave of Allaah and giving the names ‘Abd-Allaah and ‘Abd al-Rahmaan. Muslim (2132) narrated that Ibn ‘Umar said: The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “The most beloved of your names to Allaah are ‘Abd-Allaah and ‘Abd al-Rahmaan.”
And Allaah knows best.