I honestly don't know. I see reasons to think yes, and to say no.
They could be remarkably artistic with brilliant use of background visuals, colors (which the remastering butchered), clothing, and even names on tombstones, but it seemed to me they stopped trying so hard around season 3 or 4 (or getting silly over the top like when they had Buffy dressed as if for Sunday School when meeting Faith to show Buffy was the good girl), and a lot of things they said they never thought of. I suppose it depended on whoever was on production and/or how many other irons said person or persons had in the fire.
Joss seems to like to slip in easter eggs referencing classic books and shows.
Brian could just as easily be the first name to come to mind. It could even be unconscious, they knew what was going to happen, were thinking "brain" and when needing a random name, "brain" got switched to "brian" without them being consciously aware of it. Or maybe it was deliberate, don't know.