My first name is roughly pronounced as /Maanya/.
In Persian language, the name Monia is created in two forms:

-- Maan + gaah which over the years has turned to Maanya: means a place for tranquility.
-- Maani + yaa (aa of relation) which means thinker, unique, rare.

Historically, Monia was the name of one of Artaxerxes II of Persia's rulers from Dardanian Family in 399 BC.

Source: Dehkhoda Persian Language Dictionary