I would tend to agree that "Honor" seems to be the accepted spelling of the proper name. That's certainly how I (aka Guest R O'K above), a card-carrying Dubliner of some antiquity, would spell it in referring to her.
BTW, for those not in the know, the L of M is the Legion of Mary, a Catholic organisation that did what it could to combat prostitution and other social ills, but that did have a rather conservative, sanctimonious, self-righeous image.