As far as I know they just want to call themselves Turkish and that doesn't seem an unreasonable demand to most people. Can you accept that?
As a matter of principle there shouldn't be any problem with that. But as we already said, Turks have been treating us in an unfair way. An example is Cyprus were the 18% of TCs demands 50% power and 30% land.
Personally I think we are too soft towards Turks in general. We should make it clear that what we are after is democracy, human rights and respect for each other. If Turkey wants to take simultaneous steps to achieve these things then great. If not, then not only we should not make such steps unilaterally, but we should make several steps backwards to match the treatment we receive from Turkey, because as I said we are way to soft tawords Turkey compared with how Turks treat us.