If you look at the page 1939 Register Service on the Health & Social Care Information Centre website, the site says:
The 1939 Register Service (cost recovery) enables you to request data
held on the 1939 Register for England and Wales, as recorded on 29
After explaining what data can be found on the Register and whose information can be released, it says:
Is any other data available?
If you wish to request additional information under the Freedom of
Information Act 2000, please email firstname.lastname@example.org or contact
us using the postal address below, marking the letter for the Higher
Information Governance Officer (Southport).
Further down in the terms and conditions section they say that they will also release the date the service was notified of a death, but only upon request, and only if the notification was "recorded before the commencement of the NHS on 5 July 1948".
The National Archives (TNA) has a research guide here: National registration day: 29 September 1939. In the section Only the first stage it says, in part:
Keeping the register up to date had been planned for this time, unlike
in 1915, and an elaborate, but effective, system was devised to cope
with this, using a combination of national and local registers. A
national Birth Register was set up to record every birth from 30
September, and a Current Register for people entering the country, or
being demobilised from the armed forces or the merchant navy. Anyone
applying for a replacement for a lost or stolen card was placed on the
‘Y’ Register. Identity Card numbers in these registers could be in
different formats from numbers issued from the Register taken on 29
September 1939. Many refinements were made over time, including a
complete re-issue of cards to every adult in 1943, and the
introduction of cards with photographs for certain categories of
National Registration finally came to an end in 1952, but the
individual numbers it generated became National Health Service numbers
in 1948, and remained in use into the 21st century.
The register taken on 29 September 1939 in England and Wales only will
be released online later this year by Findmypast.
A comment underneath this entry confirms that only the entries made on 29 September 1939 are being released by Find My Past:
AUDREY COLLINS Thu 1 Oct at 10:07 am
Only the register taken on 29 September 1939 is being released. Anyone
who arrived after that date was added to the separate ‘Current
Register’ mentioned above.
In this release from Find My Past, I suspect we will only see the updates to the information that were written on the original 1939 registers (similar to the way updates and notes were written on the US passenger lists, or corrections were made in New England birth registrations in the US). See update below the line.
Other updates made later that were not written on the originals will need to be retrieved via a FOIA request, according to the advice on the The Health and Social Care Information Centre's site.
Note that a similar situation exists in the USA with the Social Security Administration, where one can make a request for the SS-5 and receive an image copy of the original application form -- but if you want the Numident records, which record claim dates, name changes, and so on, the researcher has to make a separate request.
Changes in Surname
Chris Paton of The British Genes Blog confirms that changes in names such as new surnames for women who married later are written on the original registers: Review of 1939 English and Welsh register release
Noreen Giles: a cousin of my wife's side of the family. I previously
suspected that Noreen might have married someone by the surname of
Cochrane in 1940. This entry notes Noreen as a hotel chambermaid, and
in a different ink has the name Cochrane written above her surname,
which is scored out - implying that the entry was updated in 1940
after she married. In yet another ink, the name Whitby is also
recorded above her name - a possible second marriage? One to pursue
Corrected Birth Dates and other information
The article Why the Queen has been erased from this database posted on CNN Money shows a page from Buckingham Palace assumed to be the page for the then-Princess Elizabeth, with two entries redacted. On line 2, you can see corrections on the entry for HM The Queen made in green ink:
Further down the page you can see other corrections made in different ink colors and two redactions:
The image appears to be Archive reference RG101/0631E/002/x (where x is the line number in the Register). Searching for Piece 0631E and item 002 in advanced search [see update below] brings up 36 open results including His Majesty the King (Ref: RG101/0631E/002/1) and Her Majesty the Queen (Ref: RG101/0631E/002/2). Their preview says "5 more people on this record". Note that the princesses are not listed on the register next to their parents, so there is no notice in the preview about other records in their entry being closed.
For more information and background on the 1939 Register see:
Despite their earlier comments made at the time the 1939 Register was released that users could search by Piece and Item number on the advanced search page, Find My Past has made changes to discourage people from doing so. The Archive Reference number has been removed from the graphic on the free preview page you get from an individual search result and has to be discovered by other means.