The pronunciation "Burk" is not that pleasant, but I'll give the name a lot of points for its uniqueness. It might be considered old-fashioned, as it has not been popular in centuries, but I still kinda like it. Maybe the sound of it is the only thing that has kept it from being caught up in the 21st century's surname-as-first-name trend in the United States. Oh, the rarity of it. Perhaps not having enough famous bearers to present the name to the public, has also contributed to its decline. If you guys actually like it, you better snatch this name up before it gets popular. However, it's not particularly likely to catch on.
I honestly love this name in all of its simplicity and strangeness. It is probably my favorite boy's name at the moment. I think that Burke Ezra would be a great combo.
Ok, Burke isn't that great of a name (I don't love it or hate it). But it is super annoying when I see comments about what the names sound like that could be teased for. You could say that about any name, and it is almost always a stretch. I completely doubt that if you name your child Burke, people will tease them for sounding like burqa.
Gee, I hope this never catches on. It sounds quite ugly with the long schwa sound, and it's plain and boring too. Some surnames really are best retained as surnames.