What is the meaning of these names: Saima and mehnaz?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

As for the world Saema, it is an Arabic word that means one who abstains from doing something. Thus, fasting means to abstain from something. In Shari'a, it means to abstain from taking food and drink and having sex from the dawn till sunset as a form of worship for Allah's sake.
As for word mehnaz, it is a Persian word that consists of meh and naz. The first syllable meh means The moon and the 2nd syllable means coddling or pampering. Thus the word mehnaz means The moon that deserves coddling or pampering.
Allah knows best.