Suki / Sukey /
Sukie are all fine as a nickname for
Susan.
I can’t stand the Sookie spelling because it looks like it should have a shorter vowel (oo as in book rather than oo as in pool), and with that shorter vowel the word “sook” means “sulk” or “person who is sulking” in my dialect.
https://nanowrimo.org/participants/christine-seaforth-finch
http://christineseaforthfinch.blogspot.com/