Similar honors can be done to the household spirits, if you want lower mythology than the Olympians. You personally come off to me as quite Khthonic, though, so...I don't know, maybe read up on the Orphic hymns?
Typically if you follow the Greek gods then you would be normally known as a Hellenstic pagan. However if you follow a certain pantheon like a goddess or the olympians you must learn about them. I for one am wiccan but combine some of the hellenstic religion into my studies. So with that said, i suggest you learn more on which gods you feel close to, also to me you seem to come off as needy for the religion. So anyways if you want to learn more about the greek pantheons go to this website.
(btw i suggest if your serious about this search....and it's your path we cant tell u how to follow this)
If you really take a close look at all the major pantheistic belief systems (greek, roman, pagan, egyptian, sumerian, hindu, etc.), you'll realize they're all pretty much talking about the same deities but just with different names and different depictions.
Just do your research and find what makes sense to you.