Definitely [name_f]Cleo[/name_f].
Definitely prefer [name_f]Cleo[/name_f]. Looks more complete and is a more widely used spelling, I ebelieve.
I love both! I prib prefer [name_f]Cleo[/name_f] but [name_f]Cleo[/name_f] is a nickname and [name_f]Clio[/name_f] is a name in it own right , if that bothers you? As you say both do have completely different origins as well. I know some [name_f]Cleo[/name_f]'s get frustrated with being confused for [name_f]Chloe[/name_f]'s, I am not sure if [name_f]Clio[/name_f]'s would have the same problem.
[name_f]Cleo[/name_f] is my preferred spelling.
[name_f]Cleo[/name_f] looks better.