Although the warhammer/holy symbol you now have isn’t magical, if you wish to name it, by all means, name it something meaningful. If you don’t want to, that’s fine, too! Something like “Forgefire” or whatever. Again, it’s entirely up to you!
Just in case you’re wondering why I can’t let it be a magical warhammer, just yet, that’s just the game mechanics. That, and you have a class feature that does it anyway. Anyway, I hope you didn’t mind the “cut-scene”-ishness of this prelude. You’ll have way more player agency from now on.
And remember, you’re level 2, now, so update your template to reflect that and update your character sheet thread.