I was told that the name Zaki has multiple meanings depending on it being spelt with the Arabic letters “zay” or “czaal”, please advise for all cases.

The word may be pronounced with a 'zaal and 'dhaal'. The meanings of both
the letters are different.

Dhaal (Dhakiyy) means to be intelligent
Zaal (Zaki) to be righteous and clean hearted.

and Allah Ta'ala Knows Best

Mufti Ebrahim Desai