Greek surnames usually end in an S. And Milioti sounds Italian.

According to her IMDb profile, she's Italian.
Don't let anyone ever make you feel like you don't deserve what you want.

Her surname IS Greek !

Wikipedia states that she is partly of Italien descent, I can't find anything about her being Greek.
But she is a great choice for the role, because she has to fit into a group viewers have become accustomed for eight years, and she does so very gracefully.
Her screen presence is amazing and her interaction with Teds as his big love is incredibly natural.

Makes a lot of sense.
When I first saw her and her name, I thought she is Italian origin until I read Wikipedia saying she's Greek origin.
Seems to me from what you mentioned, she and her family are keeping with the Greek tradition.

"Miliotis" is a Greek name- I even know someone with that name. The feminine version of the name is Milioti, but that's usually done in Greece, where the woman's last name has the feminine version, making it slightly different from her father's. Here in the States, Greek daughters stick with the masculine version of the surname, so that everyone in the family has the same one, and therefore there's no confusion with documents, I.D., etc.
Anyway, perhaps an ancestral immigrant of hers changed his name slightly to make it less Greek-sounding. I know plenty of Greeks who've done it.

Many Greek surnames end in "s" and many Italian surnames end in a vowel. I would've guessed Italian but Wikipedia states she is of Greek descent.

Hmm, I would guess her surname was Italian. She's prolly a good ole American mutt.

That's what I thought when I saw her name, but in in Wikipedia it says she is from US