I'm about halfway through The Iliad now. I have a hypothesis that the two Ajaxes are the fossilized remains of a comedy bit. I'm imagining a storyteller of the old oral tradition playing up the confusion about which was which.
"O great Ajax …"
«What?» „What?“
"I mean •Greater• Ajax …"
„Me?“ «Me.»
"Telamon's son. Look, Oilean Ajax, you're fine. Swift even, but we need Muscles here to scare off some Lycians on the walls."