So what we know is Dora Louise was calling herself WHITHAM in 1939 just three years after her marriage to F.A. Townley.
There is a birth reg. on BMD for:
PETER J.TOWNLEY born 1941 Dec.qtr. Surrey N.E.
(mmn MURRAY)...????
(maybe the J is for James after Dora L's possible father James Edward Murray).
The only marriage record I have found on Family Search is for
DORA LAOUITA TOWNLEY in Oct.1959 at POLK, FLORIDA, USA. it does not record the spouse's name.
The alteration to the name was made sometime after the initial 1939 record. These alterations, typically when a woman (re)married, went on for many years after 1939.
DaveT says a change was recorded 12th July 1951 (although I can't see that on the Ancestry image).
FMP has 2 records for Dora louise Townley born 1906.
Both have the same address and one (on p3) is crossed through in red and, in red refers to the other one on P11.
Both have townley crossed out and Witham written above it. The one on P 11 has, in the same ink and hand as the name Witham, the following marginal note (left margin)
12.7.51
NR 230 EJF
This tells us that Dora recorded her name as Witham on 12.7.51 in the Enumeration District with letter code EHV (NR 230 refers to the sub district)
Referring to the alphabetical list of Enumeration District letter codes on FMP reveals that EVF is for Hove in Sussex.
So on 12 July 1951 Dora officially recorded her name change to Witham in Hove in Sussex, where she must have been living with Mr Witham as his wife.
Thanks DaveT. See it now against the name.
For Fred's info, "Mrs. Dora Townley, formerly Dora Murray" featured in the news in 1937 (Joseph Steedon Sheldon divorce case). (Gale newspapers & British Newspapers at Find My Past)