ended up with just naming him Brig.

I've never heard any of them ridiculed for their name, or express any discomfort for being named Brigham. If you like the name go for it.

That being said I'm somebody who has a unique name that many people say "oh that musta been hard growing up with..." and they are dead wrong, I love it. But some personality types are better suited for some names than others. The fact that you and your HCBW are so worried about it (I say this in as nice of way possible) may be a sign your kids won't be the personality type who will thrive with a unique name ( I could be totally off here, as I obviously know next to nothing about you)