Brian is Brian (but pronounced differently, something like Breen)
Wolcott is not an Irish Name, so translating it would be tricky
This website http://www.brooklynbirthingcenter.com/babyNames?ID=4973
gives it as a cottage in the woods, which frankly I doubt!
Do you know what the name means? If you do, it ought to be possible to find an Irish equivalent.