I live in Greektown, Melbourne. Which means I see a lot of Greek tats sported by Greeks. And I do plenty of looking down on the cookie cutter nationalism of biceps with inked Molon labe, and Maeanders that look a little too close to swastikas. But of course, I’m a cultural conservative, so I would say that.
You will have something more imaginative than that, right?
Tats aren’t a Greek thing traditionally, so Greeks won’t feel like you’re “culturally appropriating” anything (that’s a peculiarly American thing). And Greeks in the diaspora will think it’s a Frankish (Western) thing to do.
Of course, plenty of off-the-boat Greeks here in Greektown sport tats: unlike the diaspora, Greece itself is now part of Frankia (the West).
Like others have said, Greeks overall, diasporan or not, will tend to be flattered that you like their ancestral culture enough to get it inked. So long as it’s spelled correctly and thought through, of course—because otherwise, it’s just a dis.