Lil0 is right about Paige's last name being Larson, as it has been listed that way in the credits since she arrived, and she has been introduced to various characters by that name from the beginning.
It would be difficult to have her name be different that it is supposed to be, inasmuch as school records, etc. have to be transferred if one moves around. Now it might not be her birth name, but there is absolutely NO reason to think that Jack is Paige's father. Heck, Jack was "killed" and put on Melaswen and Jen did not even realize yet she was pregnant.
While Frankie could possibly be Paige's bio father, I doubt it. I think the father is some other jerk that Eve hooked up with in her travels. Maybe she had an affair, which is what made Frankie say, "Bye", and go back to the States. I mean, after all, he became a lawyer, and is in D.C.