Both abandoned their names, since their names were given to them in a religious ceremony and have a great religious significance to them and they both don't think of themselves of worthy anymore to carry them. Jonah took a new one, Scar didn't.
WMG / Jormungand
Jonah's connection to ScarJonah is from the dimensional counterpart of Scar's people in the world of Jormunguand. They look rather similar, cooperate with groups of people they hate and the families of both of them were killed in wars.