Finding your God or Goddess is personal and it's different for everyone. Think about you, what do you like? Is there periods of history you're drawn to? What's your heritage? These are a few things to consider. You can also observe the world around you, are there symbols that keep popping up? Is there an animal you keep seeing, or you are obsessed with?
Sometimes we might pick a deity we find cool, but a lot of the time the deity chooses you. It's nice to introduce yourself and perhaps a working relationship can form, but I've heard a lot of stories where deities seek people out through meditation, dreams, or some type of symbol.
There's this one youtuber I love who did a video on finding your Goddess or God, and she speaks about her experience, how she wanted to work with Isis and refused to listen to the Morrigan. A strong symbol she claimed not only dead ravens and crows started appearing on her front porch, but every night until she finally accepted the Morrigan, a raven would peck the window over her bed, and always on her side, not her wife's side. Once she gave in, no more ravens pecking at the window or dead crows. I'm not saying it would get that intense for you, but if you've seen a lot of dogs, or perhaps an owl started hanging out outside your window, or you've always been crazy about snakes, perhaps research if there's any deities associated with that. I did, that's how I found my Goddess. You'll know when you found your deity.
If you wish to leave it up to fate you could do that as well. It might take a long time to find your patron deity, don't get discouraged, just grow in your craft. Good luck to you.