Anachronistic. I can well imagine someone naming a child Trafalgar in 1805, especially if the family had links with the Navy. But Father Brown is a good century away from that; perhaps Trafalgar became a family name?
I dimly remember that there was a provincial-level cricketer (think, County) in South Africa in the early 1960s or even the late 1950s; no idea what he did or for which team even, but I read once that although it sounded as if he was known as Laurie, his actual name was Lorraine and he got it because of some male relative who fought there in the First World War. That's another possibility: a long-dead relative's own name wouldn't have the resonance of the battle in which he featured and maybe fell. Or, variation on Oscar Wilde, he could have been found in a handbag in Trafalgar Square instead of Victoria Station!