Maya is a very interesting name for girls with roots in more than one cultures and languages.
It a very popular name worldwide due to its simplicity, profound meanings and multi lingual origins.

Popularity stats – It was most popular indian female name for year 2008(83).
http://www.ssa.gov/cgi-bin/popularnames.cgi

Here are the meanings of the baby name “Maya” in various languages:

Hinduism
In hinduism it has multiple meanings. It means illusion, wealth, compassion, unreality, wisdom, art.

The Puranas state that this whole universe is unreal, illusionary and if we feel it real it because of the working this Maya.

The word origin of maya is derived from the Sanskrit roots ma (”not”) and ya, generally translated as an indicative article meaning “that.” The mystic teachings in Vedanta are centered on a fundamental truth that cannot be reduced to a concept or word for the ordinary mind to manipulate. Rather, the human experience and mind are themselves a tiny fragment of this truth. In this tradition, no mind-object can be identified as absolute truth, such that one may say “That’s it.” So, to keep the mind from attaching to incomplete fragments of reality, a speaker could use this term to indicate that truth is “Not that.”

The concept of Maya was introduced by the great ninth century Hindu philosopher Adi Shankara.
(Source:wikipedia)

Maya is also seen as a form of Laksmi, a Divine Goddess of wealth.

Some other references of Maya in Hindu mythology and Puranic references -
1. Maya was name of an expert architect and builder who served the devas and asuras. He was father of Mandodari, ravana’s wife.

Related names – Mayadevi, Mayavani, Mayavati, Mayana, Mayapati

Greek
Maya is the modern form of the name Maia which means “Great mother”.
Maia was a beautiful nymph and the mother of Hermes, the messenger god.

Roman
In Roman mythology Maia was goddess of fertility. The month “May” was named after her.

Spanish
It is the common pet form of the name “Amalia”.

Buddism
Gautam buddha’s mother’s name  was Mayadevi.