Well, the Skull was the one who gave him the name Crossbones, because he intended for him to be his sidekick or whatever. I guess they could introduce Crossbones without the Skull being involved, but that would be sort of strange if Cap keeps running into villains with names that reference bones.
"In this life now, you kill or you die. Or you die and you kill."
DAVID MORRISSEY FOR ROLAND DESCHAIN