Not trying to make a generalization, but I think if you named your son Brigham, people would automatically assume you're Mormon, which you probably would be. This name actually sounds pretty good, but I'd save your kid the trouble and avoid using this name as there are some people who don't particularly like Mormons.
― Anonymous User 2/23/2013
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Being Mormon myself, I've always liked this name. You can still find Brigham's in Utah, but it's still not that common.