I think there are two different concepts here.
#1 is regarding the act of giving something a name that in turn increases its power
#2 is the trope that things that have discrete names indicate that they have more power
I've only ever seen concept #1 occur in Slime.
I agree with you that it is probable that concept #1 was derived from concept #2, and that MMOs specifically are a huge influence on recent anime. However, concept #2 is a trope that exists outside of MMOs also, which is why the OP referenced DnD.
While pondering this, I became curious on where OP's 'popularized' question is coming from.
Which anime, other than Slime and TsukiMichi, have there been references to giving something a name which causes it to become more powerful?