Flumen Axonam, quod est in extremis Remorum finibus, exercitum traducere maturavit atque ibi castra posuit.
I know flumen is neuter but in this case the river is specified by a a masculine name (Axona) so why wouldn’t the relative pronoun be masculine?
Because quod refers to flumen. Axona just happens to be the name of the river.
“a masculine name.” Or feminine? (This is a genuine question, to which I don’t actually know the answer. Rivers are generally masculine, but there are exceptions, though first-declension nouns can of course be masculine. If the Axona is attested in Greek we’d be able to tell. What gender is l’Aisne, the modern name? I have no idea, and it might not be relevant anyway. —Sorry, this is boring, but enquiring minds want to know.)
But as to the neuter relative, it’s normal. The river’s name is immaterial to the gender of the relative, whose antecedent is flumen not the name. As bedwere says.
L’Aisne (both the river and the département) is feminine.
L&S has it as masculine. The OLD does not have an entry for it.