I prefer
Damian. According to Behind the Name,
Damian was the name of a
Christian physician who was martyred with his twin brother,
Cosmo, in Syria early in the 4th century. While living, they were known for treating the poor and accepting no payment for their services. Due his renown, the name came into general use in
Christian Europe. The Eastern
Christian Church considers the brothers examples of Unmercenary Physicians (Greek: ἀνάργυροι, anargyroi, "without money") and refers to those who heal purely out of love for God and man, strictly observing the command of
Jesus: "Freely have you received, freely give." There are various other famous Damians including
Damian, also called Saint Deruvian, companion of Fagan (fl.
AD 166),
Damian of
Alexandria, Egyptian soldier and martyr,
Damian, Pope of
Alexandria (r. 569–605), and
Damian of Molokai, who helped those suffering from leprosy. Irish singer
Damian McGinty is also a bearer of this name.
Although I am familiar with the Greek legend of
Damon and Pythias, too me the name
Damon primarily reminds me of sleazy vampires. I also like the sound of
Damian over
Damon.