Was Joseph married prior to Mary? If so who what was the woman’s name?
We don’t know the answer to this question. There is a pious tradition that St. Joseph was a widower with children from a previous marriage but it is not a teaching of the Church nor is it found in the Scriptures. Most of the “details” of St. Joseph’s life found in apocryphal gospels is considered highly unreliable but not necessarily completely untrue.
In some of those unreliable works it was said that St. Joseph had been previously married but the name given varies according to the work: Melcha or Escha by some, Salome by others.
Some Church fathers accepted that St. Joseph had previously been married and others rejected the notion. The Church has taken no position.