What does the name Maya mean?

It depends on the language you take the meaning from:

• In Hindi it means "illusion" and is an alternate name of the Hindu goddess Durga. ...
  
• In Hebrew, the name means "spring" or "brook."
  
• In Old Persian the name means "generous."
  
• In some Arabic languages it means "water"
  

If you mean the Maya people name comes from the ancient Yucatan city of Mayapan, the last capital of a Mayan Kingdom in the Post-Classic Period.