1939 Register

[Tickettyboo]

Looking at the full image (which we are not allowed to post). I'd say that the Mary J Gilbert's name change (in green ink) is linked to the note in green ink at the left hand side which is dated 1957 - therefore something happened around that date to cause the change in her name (would have been done by the NHS who updated the register)

The other two name changes I (at a guess) would say were done at the time the register was compiled seem to be in the same ink and writing. Maybe the person writing it down assumed that all the occupants had the same surname and were corrected by someone in the household before he got to the final name?
Matching births in Stoke on Trent District, for the younger two occupants,  have a surname of O'Brien and were registered with a mother's maiden name of Gilbert.
 
Mary J was said to be single in 1939, James was said to be married.

Its 'possible'  - though by no means certain, that these two were the parents of the younger two but for whatever reason (possibly as he was married and though didn't live with his wife was not free to marry) she was still single and using her maiden name

The nearest marriage I can find for a James O'Brien and a Mary Gilbert is in Q3 1955 Stoke on Trent District -  though that does have the bride as Mary A, not Mary J. Again this is just a theory, but perhaps by then James was free to marry and  the 1957 note related to Mary's  name change was when she notified the NHS of her marriage and name change.

NB.  Search Free BMD Q3 1955 for each name separately as James' entry has been mistranscibed as vol 6b rather than vol 9b so he doesn't appear on the same entry as Mary. - I've sent in a correction report but it will take a while to update the database

Its a theory to explore, but I'd recommend searching Free BMD thoroughly first to see if there are any other earlier marriage options for James and then try to track down when his first wife died and proceed to the marriage cert from 1955 to confirm he was a widower by then.

EDIT So sorry I forgot to say, I think your first step would be to get a birth register pdf from the GRO (cheaper than a cert and exactly the same info) for one of the children to verify the mother's first name. If it does turn out to be Mary then the above theory could hold a little more weight.
There was a death for a Mary Agnes O'Brien in 1980 , Stoke on Trent District and that lady shared a birth date with the Mary J Gilbert, later O'Brien, on the 1939 register

Boo

[peterpiper]

Boo, Thank you very much for your time and effort.
Your theory's are facts! researching my own notes from a few years ago, which I thought were lost,
all ties in.
The marriage of James & Mary in 1955 is James's 2nd, he "split "from his 1st wife sometime between 1913(the D.o B. of his 1st Son) & the birth of Joseph in 1926, his 1st marriage was dissolved about 1954, his 1st wife went on to re-marry in 1955,
So, to my reckoning, James's Son from his 1st marriage (my Dad) is half Brother to Joseph & Norah, making their offspring my Half Cousins, some of which may be still living, or doesn't this count with the illegitimacy problem?
Once again,
Thank you very much
pete