Do you speak Greek? I only ask because Antoniou is a surname (I can tell from the way it is conjugated). So Antonis Antoniou would be first name, surname.
Don't mean to be a nuisance, but some of the suggestions above are not Greek.
It's Ilias, not Elias
there is no Greek Theo pronounced Tay-o, unless you mean Theos which means god and is not a first name,
Giorgos is not pronounced Your-go,
Nicholaos is shortened to Nicos, Nico is the conjugated form of Nicos,
it's Costas
Vasilis
and Savvas
the conclusion of which is that things may go a bit wrong if you don't have a knowledge of Greek.
Having said that, what Greek names do you like?
Popular ancient Greek names include
Socratis
Aristotelis
Dimosthenis
Aristidis
Periklis
Odyseas
Ektoras
Ionas
Frixos
Very popular modern ones
Nicholaos
Giorgos
Giannis
Christos
Constandinos
Dimitris
Vasilis
Stavros
Other ones:
Andreas
Miltos
Athanasios/Thanos
Charalambos/Babis
Manos
I have run out of relatives and friends at this point!