What do you think of these character names?

I like these names, except it's pretty obvious that you were inspired by Twilight when you made them. I would consider changing Jasper to something else. That name combined with "Bea" (which is similar to "Bella") screams Twilight. For the girls' names I really like Beatrice and Tierney, but Seraphina might be a little much. That said, it also depends on the character. The name "Seraphina" could suit your character very well. I would just be careful not to overdo that romantic quality.