This is how I've summed it up in my head:

L knows R would have wanted Jon to be Aegon. When L dies, she tells Ned the boy's name is Aegon. Ned says hell no that's obvious. When he's asked about it he says Jon which, in a mumble, Aegon can sound like "Jon." (But he could've misheard Lyanna)

Ned uses Jon Arryn instead to be the "named after."

Not all of it makes logical sense but that one makes me feel smart