Migrants don’t claim Greece as their homeland because they know its the homeland of Greeks not their own ancestors. They come for more money in Europe not integration. They either end up either moving on or taking trips back to their actual homelands.
For instance many calls basketball player Yiannis “Greek Freak” because US press started to use this name, If you ask Yiannis himself he has a love of Greece but still sees himself as a Nigerian. He moved to US because the money was better. Now he’s American but still see’s himself as Nigerian much like you still see yourself as Palestinian not an ethnic Apache.