Q: Do I have to go back and relearn the proper name for each chord?
A: the only reason to know names of chords is to communicate with other musicians about what you're doing, particulaly when working together. so the next time you're working with another musician, especially if that chord comes up, you could say, 'hey what do you call this chord? i call it blah blah' and they might say 'oh i think most people call that blah blah' so now you might try calling it that the next time you are in a collaborative or working setting, and when you are by yourself you can continue to call it what you want. OR they might say 'oh wow, i never had a name for that chord, i like the name you gave it, i think i will start calling it blah blah also'