AITA for keeping asking the girl I'm seeing about her name tattoo?

So I’m (27M) dating this girl (24F) for about a month now, and the last time we got together I noticed she has a very small tattoo on the back of her neck. I had never seen it before because it’s covered by her hair. Now here's the weirdest thing: she has MY NAME tattooed. So obviously the first thing I thought was that she made a tattoo after me, which would be insane given we’re only going out for a few weeks and this is still a casual relationship.

But she told me that is not about me, it’s about someone else that has the same name, just a coincidence. I looked closer and noticed the tattoo seems old and faded, so it definitely wasn’t done recently. Either way, I was obviously intrigued so I asked: “Is someone in your family?”. And she just said: “no”, and didn’t provide any additional information. So it was clear she didn’t want to tell me who this person is or was, but now there’s suddenly this missing piece of information about her and I simply can’t let this go. So I kept asking her: “was it a friend? was it an ex?” – until she lost her patience and told me it’s none of my business. AITA for keep pushing her to tell me who it was?

Also worth saying: she has no other tattoos besides this one, so it seems even more meaningful.