I wonder if William Gavin is the William Smith showing in Sheffield in 1881 with the Gavins as age 8 born Suffolk? In 1901 I think Daniel Gavin's sister, Mary Theresa is recorded as Theresa Gavin, a boarder in the home of William Smith 27, carter born Sheffield. Coincidence?
William
Hi Millmoor, yes I too thought that William Gavin was likely to be the William Smith in the 1881. Possibly the illegitimate son of Mary Ann Gavin (nee Smith), William and Mary Ann are both noted as born in Suffolk. I hadn't spotted the 1901 for Theresa Gavin and William Smith, it could well be the same William.
William Gavin's criminal record is a good find too!
Apologies, I've been away from my computer for a couple of days. Many thanks to Millmoor, Janan and Jool for the information, particularly the newspaper cuttings.
The William Gavin thing is interesting. I had noticed that William Smith aged 8 had appeared in the Gavin household in the 1881 census. I knew that there must be a connection to Daniel's mother, Mary Ann Smith because William was born in Kedington, 4 miles from the Suffolk village where she was born. I thought that he may have been a nephew or other family member but now you mention it, an illegitimate son seems to be the obvious answer. That might explain why she left home and moved to Sheffield.
I still can't find any marriage record for Mary Ann Smith to Joseph Gavin, neither can I find a death record for her.
However, my original question has been answered. My great grandfather had an extensive criminal past and he used several aliases. He married under one of those aliases and that's how I got my surname. I suppose that finding someone famous in your family tree would be great but to have some dodgy relatives is equally interesting. Giverin is quite an unusual surname so for Daniel to use it as an alias, one has to assume that he must have known someone else with that name. We will never know who it was but I'm happy with that

Thanks again to everyone for their help.