It's up to you. I usually do last names, but it's not a huge deal if we don't use one.
Io Persephone is actually a GP of mine. So, I love that combo right off the bat.
I also like all of those names you've listed among:
Alexandra
Ariadne
Aurora
Calliope
Daphne
Maia
Niamh
Phaedra
Phoebe
Rhiannon