Sioned yw priodferch Alys.
In the newly released iOS app, the only answer marked as correct is "Sioned is Alys's bride". However, "Sioned is Alys' bride" should be correct, as should 'Sioned is the bride of Alys'.
Within the app there is no means of choosing 'My answer is correct' for this question.
The website asks different questions so it wasn't possible to discuss this directly from the question.
This issue is almost as fraught as the Oxford Comma! In any case, "Alys'" should be allowed, although "Alys's" is probably better, particularly as that is closer to how people would say it.
The Penguin Guide to Punctuation supports this:
'A name ending in s takes only an apostrophe if the possessive form is not pronounced with an extra s. Hence: Socrates’ philosophy, Ulysses’ companions, Saint Saens’ music, Aristophanes’ plays.'
Nevertheless your mileage may vary!
As a total aside; for some reason this amused me from Wikipedia as being a typically British example of pragmatism:
As the Palace of Westminster is still technically a Royal Palace, a convention has been adopted that any commoner who dies within the Palace is officially recorded as having died at St Thomas' Hospital to remove the need to convene a jury of members of the Royal Household under the Coroner of the Queen's Household.
For anyone (esp. Americans) who may be confused, the Houses of Parliament are housed within the Palace of Westminster.
Yes, it seems rules have evolved since I was at school where I was taught that neither should an extra 's' be added in writing, nor should it be pronounced - except where it would cause confusion.
It seems modern practice/guidance is that an additional 's' should be added after the apostrophe if it would naturally be pronounced that way. Interestingly, there is a very prominent disagreement with this in large letters across the Thames from the Houses of Parliament; "St. Thomas' Hospital". :-)
I don't think Alys' bride is correct -- as far as I know, singular nouns (including proper nouns) ending in s take 's as usual to form the possessive, with the exception of a handful of "classical/historical" names such as Moses', Jesus'. Alys is not quite in that league :)