I am relatively inexperienced at the game and doing some enchanting.
I am level 12 with no enchanting or smithing perks.
I have a dwarven bow which the game will allow me to enchant with fire; but will not allow me to name.
The option to name does not come up.
The game will allow me enchant a hunting bow (superior) with fire and also name it.

So why will the game let me enchant & name the hunting bow, but not the Dwarven bow?

Are you typing in a name with the existing name of the bow still there? There is a character limit for a name.
Did you choose all other options before trying to name it? I don't think you can name it before choosing a soul gem type, etc, but not 100% sure.
If typing on a keyboard, don't use your mouse as it can mess up. I always use arrow keys.