They didn't speak Greek. They spoke a bunch of languages that predated Greek. There was no place called Greece then, and the people of the time had all sorts of words for the various groupings, but Greek/Hellene wasn't one of them.
It's best not to transplant our national identities into the past where they don't make sense. Nationalist mythologies can and have been used for some pretty awful things.
Mycenaeans spoke Greek. I've didn't say anything about national identities. If you don't think there was some ethno/cultural/religious/linguistic category in the rough shape of "Greek" before they started calling themselves Hellenes... that's weird.
It's best not to transplant our national identities into the past where they don't make sense. Nationalist mythologies can and have been used for some pretty awful things.