Is there a couple name for Barney and Robin?

Of course!! Their name is Swarkles and it has been for a while now.

Swarley+Sparkles=Swarkles.

Or I mean I guess you could go for BRo Love, but it's definitely not the most official name and does it really make that much sense? Of course the best term to describe Barney and Robin is bro's with benefits but I'm just saying that NAME doesn't make sense really. I think it's Swarkles and I ain't changing my mind about it. :)

There's also Brotp(Barney+Robin=One True Pairing/they're Bros)
there' also:
-Barbin

CBS did a video montage of Barney and Robin. They called it Bro-love. I think considering the characters personalities Bro is the perfect Robin+Barney name

Rarney

yeah there is BRo

I've read the name Robarney in a lot of interviews with the cast. So that might be somewhat official.

How about Roney.

yes there are quite a few such as.----
.BRo
.BRotp
.Bobin
.Rarney
.(and my personal favourite) swarkles
there may be more but these are the ones that i know :)

There are a few but nothing official or anything like that. Some popular ones are Swarkles, Bobin, BRo, brOTP

Yea there is there's swarkles (swarley and sparkles), brolove, brobin.

Their is Swarkles.
Barney has called them Barnman and Robin.......
BROTP
Robarney