Are there any mods that allow to name a weapon you have modded( similar to morrowind and oblivions enchantment system)? I.E as soon as you apply a mod to your weapon an option to give it a custom name appears. I know you can do it in the geck but that kinda defeats the immersion.

Not possible, modded weapons don't change base form unlike enchanted ones.

Cloneform + String functions

when we get those...

Yeah, although cloneForm doesn't save (they used the enchant cloning code to do that in OBSE, and it's been removed) so NVSE co-savefiles would need to be implemented too.