There's quite a few and some seem straight forward. Which ones are giving you trouble? I study classics and I'd be glad to help.

I don't understand entirely what you mean by "correct." Kleomenes is no more correct than Cleomenes--the only "correct" way to write that name is in Greek, "Κλεομένης." Cleomenes is the Latinized form of the name, and Kleomenes is the form that attempts to mimic Greek spelling, but using Latin letters nonetheless. Neither is really more correct than the other, it's up to personal preference--the lack of several letters in thr Latin alphabet that exist in Greek means that it's just as wrong to write Kleomenes.