Well, this is me, and feel free to tell me I don't know wtf I'm talking about.
I try very hard not to get too hung up on identity. In the end, we're still talking about people. Not people like we are, but people.
I'm of the opinion that the idea of "old" gods and "new" gods misses the point. It's remotely possible that I could call on Athena, to use TheHumingbirdWizard's example while piggybacking on what she said, the way she was called on back in "her" time, but even if I could - and I can't - I'm an American woman in a modern age. Context is entirely different, and context is everything. Far better, and far more honest, to call on her in a way heartfelt to me based on whatever research and person gnosis I have, with my best understanding. In my experience, if she feels like bothering (actually, I've never had a problem with Athena in that regard, but as a hypothetical), she'll then go on to explain to me exactly how I should talk to her. Just like getting to know anyone else. Whether she's changed from the past or not is kind of nosy on my part, actually, I sure as heck don't show my high school pictures to just anyone. She is as she is to me, now.
But I also think that it really doesn't matter nearly as much as most people think if I'm actually talking to THE ATHENA. Perhaps she is. Perhaps she is a spirit of a lesser power or newer birth who identifies closely enough with the Athena of the Greeks to feel the right to step into her sandals; say, a priest or priestess. Perhaps she's a delegate from Athena. Perhaps she's my grandmother who always really liked the name, and who also felt a connection to the goddess and that's the only way I'm willing to talk to her spirit. (Well, not my grandmother personally, but theoretical grandmothers.) Yeah, if there's malice, harm, or trickery to a destructive purpose, shut the relationship down and start again, but frankly, we very rarely actually need A GOD for what we think we do. I kind of wonder if some find it insulting that we think our petty concerns are actually that big, when a simple request to our most recent new ancestor or the spirit of the tree in our backyard would do just as well. If a spirit is pretending to be a god, and it's a good, healthy, and successful partnership with you, than the rest is, imho, between them and the god, and it'd take a braver soul than me to pass judgement on it.
Same thing for patrons, though my experience is that I've yet to choose a patron that hasn't chosen me first. If it's healthy, mostly does what it's supposed to do, and is positive, go with it. Delve deeper as you get to know your patron, don't be an arrogant jerk up front. You called, they came; by choosing to call a specific god, you've specified what you're looking for. That said, though, I absolutely think gods and goddesses can be patrons, and may or may not then be what their patronee expects. (Mentee? You get the point.)