I heard the Uzbek name Oibek/Oybek recently. I know its equivalent in Turkish is Aybeğ ایبک (like the famous Kutbiddin Aybeğ of India) because oy = moon and bek = beğ
What is the meaning of Aybeğ? Does it mean the lord of the moon (that is, God)?
No. Bey/Bek is not God. It's a lord of a land. Ay means the Moon, but it's a common particle in many names and has the connotations of being beautiful, pretty handsome and perhaps pure. It is not to be understood as the lord of the Moon. There are many such names: Aybars, Aygül, Ayhan, Aysu, and others that I can't think of right now.