Sorry I cannot help with names for Frodo or Bilbo, but I was intrigued by your query on whether they would have gone to Valinor.
I believe they would indeed, and probably were honoured with an audience with some or all of the Valar. It would have been right for Gandalf (as a Maia on a mission), Elrond (with his Maia and High Noldorin descent), and Galadriel (symbolic of the redeemed and reconciled Noldor) to have this privilege, and I feel the hobbits too would have been honoured for their extraordinary deeds.
Tol Eressëa would have been an ideal place for the hobbits to dwell. Bilbo, in particular, would have been right at home there.
Now this really surprises me, but Elrond's reunion with Celebrían is something I had not considered. It would make a fine subject for one of your beautiful poems.
Galadriel's reunion with her father (not to mention her daughter) is something else I hadn't thought about. In time I might even tackle that myself, but only after a good deal more book-work. I'll pay attention to the archaic accusative, as Finarfin may still have some sharp words to say about the Kinslaying.