The gods are the powers of the unfathomable universe (all that is). But that doesn't mean they are not thinking, feeling beings. Dionysius was worshipped a lot like Jesus. There was a big following. If you believe in reincarnation, you may consider that you lived during the time of his worship and he is merely calling you back to him.
Another possible reason is simply the law of attraction (like attracts like), we naturally feel a pull toward those like us, so as was said above me, you may share similarities to the deities you feel closest with.
However on the topic of Hecate/Lilith. I've noticed something and others have to. Hecate/Lilith has been attracting, and in my opinion, has been calling to people. Many including myself, have felt a sudden pull to her without understanding it. Even with no prior interest. I'm not even going to guess why. I don't think we are "special" I just believe we are "open" and accepting of her therefore we feel her call. I highly suggest working with her, she is up to something important.
They say the gods are only as strong as the belief of them. Their believers give them strength to influence on the physical plane. So maintaining a more personal connection with followers benefits them. They want you to know they're there to reinforce your faith, which reinforces their strength. They help you and you help give them the energy they need to do their work. After a while of loyalty from you, most deities really do gain a personal attachment to, like a parent to a child and sometimes after years/lifetimes of commitment, they consider it a close friendship.
The same deities go by various names depending on culture. So you may wish to look into that.