Spoilers for those who haven't played Persona 4.
Now, this may have been talked about before. If it has, my sincerest apologies. But going back into Persona 4, I had a bit of a recollection at 4 in the morning for some reason.
There was the term "phantom thief" in Naoto Shirogane's social link in Persona 4. It was apparently an act put on by her grandfather. Considering in Persona 5, Shirogane was directly referenced, with Tohru Adachi being indirectly referenced on the TV with what appears to be an interrogation or trial. This had to mean Persona 5 was taking place around a similar time.
Now, if I remember correctly, throughout the party's adventures, the Phantom Thieves became well-known throughout Japan and even had some traction internationally. It's very likely our cast in Persona 4 had heard of them. So possibly her grandfather did as well and maybe just decided to use that?
Don't get me wrong, I'm not trying to make any full theories or anything. It's very likely Atlus didn't think that far ahead and just thought "phantom thief" was a cool name. I don't know, I know the past games can't really acknowledge future games. I just thought it was quite interesting to point out.