The name of the child on the 1939 Register that you can see may be the middle name and not the first name.

Edit to ask: has anyone found a marriage for this child yet?

Yes, there is a likely marriage in 1958 with a middle initial matching the given name from the 1939 Register, but I don't want to post too many details on here as the person may still be alive despite their 1939 Register record having been opened.

Ahhh right.

Ah, just checked. The Q3 is in Oldbury, Worcestershire but the two names are correct.
I can't find the birth for the Q1 1937.

I think the one Maggie found was registered in the mother's surname and was in London.

The birth I found was Jan 1937 Southwark London.

Received certs today which confirms Edith Mary as Ethel's mother.

9 Feb 1930, Maternity Home, Poulton-cum-Spital. Ethel, Girl, Father's name and occupation left blank. Mother, Edith Mary Sharratt, Domestic Servant of 1 Walker Street, Hoylake-cum-West Kirby U.D. Informant, E.M. Sharratt, Mother, Maternity Home, Poulton-cum-Spital. 19 Feb 1930, G.H. Tomlinson, Registrar.

18 Apr 1953 after banns. John Neilson, 22, Bachelor, Plumber, 22a Green Street, Stonehouse, Lanarkshire, Scotland. Father Walter Neilson, Miner. Ethel Sharratt, 23, Spinster, 26 Curzon Park North, Chester. (No father's name recorded). Witnesses M. Smith & R. Cuthbertson. Ceremony conducted by H.J. Williams.

From the information on the marriage cert I think John's parents were Walter Neilson & Elizabeth Frew (ScotlandsPeople Marr: 1930 Ref. 656/5 Stonehouse) and that John died in 2017 (ScotlandsPeople Death: 2017 Ref. 577/841 Hamilton), a year before Ethel (ScotlandsPeople Death: 2018 Ref. 566/393 Bellshill). Hamilton & Bellshill are very close to each other. One may have died in hospital and the other at home.