I fear there are too many ifs and buts to make much progress with this.
Although it is difficult to find a reason why he should choose Dorset if he wasn't born there, it is far from certain that he was born there. It is clearly worth exploring though; this site is good:
http://www.opcdorset.org/You probably have the following:
1. There is only one George Henry Pollard born at about the right time (in Sheffield). His father appears to be William, a coalminer.
2. He could have changed his name. If it to hide something, you are probably stuffed. If it is because his mother remarried and he adopted his stepfather's name, you may be lucky.
3. There are at least eight George Henry Xs born in Weymouth at the right time! One of them is illegitimate (son of Jane Grant) which looked a possibility, but he died soon afterwards. You may want to follow up some of the others (Guy, House, Trantum, Bussell, Lee, Towells, Williams,,,) to see if there is a marriage to a Pollard.
It is not uncommon for an illegitimate child to invent a father's name on a certificate (particularly if it is a long way from home so no-one can check) but there are other reasons for name changes.
Good luck.
Richard