nitpicker, these actually seem like titles rather than names. Nor is Shlomo Zalman a proof, it is the vernacular for Shlomo, similar to our Solomon. That is actually another possibility of how the trend started. First the nickname was added later as a title, and then it became part of the name and was given at birth. Later, the second name became more random.
Perhaps we can point to Yaakov Avinu, Moshe Rabbeinu, and Shlomo Hamalech, although we never find them being called more than one at a time.