[Rune Son of Bjarne]

I am not a big fan of puns, so I would probably go for "Blades of Westernesse" or "Thuringwethil".

The first is very obviously handy, in fact I think everything could be made better with a blade of westernesse, and Thuringwethil is both handy as a messenger and later as a disguise.

Eorl the Young and Anduril could be outsiders for me, but they seem to have very specific application. Anduril was handy for Aragorn, but I doubt that anybody else could have used the sword to the same effect.
These things doesn't really matter, but it weird thinking like this that would determine my decision.