Bragi was probably based on a real person, the skald Bragi Boddason, from the 9th century. He was deified after his death.
In Lokasenna he was accused by Loki of avoiding battle; this may have to do with the fact that Bragi customarily is awaiting the slain in Valhalla in the wake of conflict.
A Bragarfull was a sacred cup over which people swore oaths, honored dead kings or kinsmen. Newly enthroned kings drank from a Bragarfull.
Alternative: Brage