Greece didn't claim the country for itself, it claimed the name for it's own northern province.
The country of Macedonia was part of a region generally called Macedonia for over a thousand years, as the initial named unit of Macedonia (which was in Greece) expanded to cover a wider area.
Besides I think the people in Greece-Macedonia are happy being Greek.
Macedonia is part of the Greek identity. FYROM (still the official name until the agreement gets implemented in a few months) have been claiming this Greek identity by misappropriating history.
Think of it as a trademark violation.