Answer
(Fatwa: 1146/718/L=1433)
Shiza [شیزا] means: the wood of ebony. (Misbah al-Lughat: 459) while Maheen [مہین] means: Fine, thin, weak, lowly. (Firozul Lughat)
In fact this name is not much good as per the meaning. If you keep any name among the names of the holy wives, holy daughters of the Prophet and Sahabiyat then it shall be far better. Good names have effect hence the holy Prophet Muhammad (صلى الله عليه وسلم) used to advise to keep good names and he used to change bad names.
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband