But in Jane Eyre, Mr Rochester signs a letter as 'Fairfax Rochester' and he refers to himself by that name a few times. Yet his first name is Edward...

I'm just wondering if this was in any way a standard way of signing letters, thus 'Fitzwilliam Darcy' doesn't mean his own first name was Fitzwilliam, just his middle (mother's) name...

I believe it used to be that boys had their mother's last name as a middle name, whereas girls had no middle name. When they got married, their maiden name became their middle name.
So Elizabeth will be Elizabeth Bennet Darcy, and their eldest son will be "John" Bennet Darcy (or Charles, or whatever...)