First of all, he was baptised as Robert James (not James Robert) and the baptism entry would indicate the parents were not married - usually, when a couple were married, (as you will see from other entries on the page) the mothers maiden name is not given but in this instance both full names are given.
I cannot find that his birth has been registered under either surname, nor can I find him in 1891 or 1901.
Since his parents clearly not married his surname should have been Matthews.
Then, in 1911, we find a Robert James Matthews b.1883, with wife Jane and 2 infants (births index indicates her maiden name was Hancock). Son William birth registered 1910 as William Handley Matthews, mmn Hancock.
As with Robert James' own parents does not look like he and 'wife' Jane nee Hancock were ever married although he was Matthews in 1911 and children as Matthews in 1910, 1911 and 1912. What happened after then I don't know as can't trace them as Matthews after 1912.
Annette