He started off as CeeCee the Hextech Engineer. She was a mechanic from Piltover who used a Hextech-powered shield. This incarnation suffered from gameplay complications and, slowly but surely, became Braum.
Braum himself was at first a Demacian but this Braum was deemed too serious for his jolly defender theme, so he was moved to the Freljord.
The name was probably changed because Braum can actually move during the ability's duration.
Braum's legendary status through the (at least over five) generations as well as the lack of significant aging (if the former is accurate) give way to the theory of him being an Iceborn.
The other theory is that he is not a flesh-and-blood individual. Instead, he is the embodiment of the less cruel side of the Freljord, whose 'existence' is tied to the people's fascination with him and his feats.
Braum's speech is unusual in that his has a heavy accent compared to other Freljordians as well occasionally referring to himself in the third person.
Braum features a lot more champion interactions directed at people he's actually to meet down in bottom lane (Marksmen and Supports) compared to ones directed at lore-related characters.