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If it's Greek the spelling is problematic. A letter G followed by an E or an I is pronounced like an English Y in Greek. So the -GE- sequence and the -GI- tend to be spelt with a Y in Roman script. So I would expect to see Vayenos.
There is a Greek word vayéni, which means a barrel or cask, for holding wine I think. Perhaps Vayenos, if that's how the name would be pronounced, means a maker of such containers.
Only a guess.