(Forgive me, I'm not a comics expert.)
We have the enchantment by Odin on Mjolnir:
Whosoever holds this hammer, if (s)he be worthy, shall possess the power of Thor.
So that means there is a power, separate from the original Thor, called The Power of Thor that Mjolnir confers.
This is bolstered by the fact that we have the new Thor, Jane Foster who also wields the Power of Thor and goes by the name Thor.
- Did the original Thor already exist at the time Mjolnir was forged?
- Was the power named after the man or the man after the power?
- Did first Thor ever have any other true name? (For real, not an alias on Earth.)