Just to give a bit of context; say I'm playing a song in a certain key, F major. and let's say I'm playing the I IV V chords. I'm playing a song I learned by ear, right now it happens to be bicycle built for two. But I've been doing it so I mainly remember the chord shapes and their sound. But I don't try to remember the chord names that I play.
But should I make an effort as I play to know the name of the chord as well as the scale degree? So, I might think to myself "now I'm playing the IV which is a B flat major" as I'm playing it.
Would the only benefit of this be so that I can play the same song on another instrument?