I think Trent is just his middle name, not part of a compound surname, middle names are never sort operands on this side of the pond. So IMO "D'arby" is definitely the correct search criteria, which narrows it to "D" or "A." In his case, his mother was named "Darby," so in my view the D' is just an affectation, not an article
I would shelve it under D.