LB: IMHO, there is a difference between a person’s name and Yerushalayim. I have never heard anyone shorten the name of Yerushalayim.
Shlomo is the name of Dovid Hamelech’s son and has nothing to do with the name Sholom. In addition, Sholom is one of the names of Hashem and I don’t anyone who uses a shortened version.