Have you found Annie and her husband in the 1939 Register? We aren't allowed to post details but they appear to be living seperately and finding them might explain the AKA Roberts ref on her death cert
Have you got her in free index for us?
Best I can come up with!

Annie Wheeler (Bromley), born 1902
at 4 Middle Street, Bethesda U.D., Caernarvonshire
Oswald Roberts and 2 more people are on this record
Oswald born 1891 in free index.
I think maybe she is Annie Bernley on ancestry? Not sure what it says, and we aren't really allowed to comment.
may give it a go if the birth certificate doesn't give us the information.
But which birth cert?
Is this who you think Annie is in 1911 (free index)?

Annie Williams, age 8, in Llandegai, Caernarvonshire, parents Thomas and Jane
https://www.familysearch.org/ark:/61903/1:1:X7VV-9GDMother might be a Jones. Difficult to be sure! Thomas and Jane possibly still alive in 1939 and also in Bethesda U.D.