Is there any data concerning the historical use of Welsh names in Wales?
Yes; the same data as there is for all names in the UK, i.e. parish records and wills, deeds, tax lists, etc.
For example, would
Mair as opposed to
Mary and
Gwilym as opposed to
William have been standard in Victorian Wales?
Both
Mair and
Gwilym were in use in Victorian Wales, but
Mary and
William were a lot more common; in some instances this would be the parish recorder (usually the local vicar or a curate) writing the name down in English, but they were just generally very common names throughout the whole of the UK.
Were names such as
Rhys,
Gwenllian, and
Gruffudd common throughout history in Wales, or only during the Middle Ages and after the Celtic Revival?
Yes, those particular names have documented use in Wales (under various spellings) throughout Welsh history, and in the neighbouring counties of England, too.