Yes it does say Rowe on the BT, I only thought because a Cowley later marries a Howe and I noticed the prevalence of them in Gainford and Denton. I've had problems with mistranscribed BTs before and on other occasions they've missed out a year, a lovely resource, but annoying at times. Trust it to be this line with all it's inherent problems, the Cowleys were easy to track except for the original George and Lovehannah who were a right pain until I found them in Denton. I still can't find the deaths of either to this day.
As to Joseph, he would be old enough to have moved on for work by 1841, he may have always lived with his Burnside relations though, perhaps sent to work for them? I find it odd that neither he nor his mum took on the name Cowley for appearances, nor did he take Howe. There's another odd child related thing with George and Lavinia Cowley in that their son George's first son John always lives with them on census, not his own parents and never migrates over to Billingham like the rest of his siblings. He eventually has a daughter called Lavinia the only time the original name is used for a child rather than Vina,Vinah, Vienna, Vianer etc. Very odd and not something I've seen before. George incidentally would be the same age roughly as Joseph despite perhaps being his half uncle. I'm sure there must be other children for George and Lavinia but I haven't found them yet. I can't read the Denton BT baptism for George but it is saying something about a certificate and Croxdale, perhaps they moved to Walworth from there.
Dan