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There are several ancient sources about the two names (actually there is a third but used very little nowRomi-i) , none of them better than the other, but the name/word Greek in few of these sources is related with a negative meaning. But since it has to do with sources written by the Romans, the ones that actually gave us this name, it is natural to have such a meaning. As I have mentioned all names have ancient origin (greek most probably from an old town at Viotia or a hellenic tribe) . But it is a name, that for most people abroad has only the meaning of what they think it describes. If they think people living here are bad, it doesn't matter how you call us. Of course the etymology of a name has a special weight that is used by historians and some times the politicians. For instance, the Arabian and muslim world know Greece and Greeks as Younan and Yuns, a name coming from an othe ancient hellenic territory Ionia (placed in Asia Minor territory, where today is Turkey). So in the case of Greece and Ellada, both names are justified, since in fact they have the same ancient origin.
