Dog ownership

Not sure if this really counts here? I guess more so advice or if anyone’s been in the same sort of situation?

I’m based in Melbourne, and about 1.5 years ago, a friend of a parent purchased a puppy. With first vax and chip. Said puppy was “too much” and they gave it to me. I love this dog. We spend every day every together. She’s up to date on all vaccinations and everything she could possibly ever want or need. Now here’s my dilemma. Getting her into my name. The people who bought the dog never signed her into their names. So the chip is still registered to the original owner, who wasn’t or isn’t a registered breeder so I have no contact information for this person. My parents are no longer in contact with the person who gave us the dog, nor do they live at the same location for me to pop in and ask if they still have the original ‘breeders’ number or address for me to get a signature to get this dog in my name. The vet can only give me so much info. Which is just the town the chip is registered too, they can’t give out the name or number assigned to the chip, which is okay, I totally get that. But where do I go from here? She’s an inside dog so I don’t fear she’ll run away or anything but I just want her to be registered to me. I can’t locate the OG owners, I can’t locate the ones who bought her then sold her to me. I’ve asked the vet if they can even contact the original owner themselves to prove they’ve given her away and put something down but I guess legally they can’t? I don’t know, I’m just stuck in a pickle on a dog I’m in love with, that I don’t ’technically’ own despite being together since she was 9 weeks old and paying for everything possible.