Go to the account settings (Long-touch on the account name in the accounts-list view), choose "Account setup", click on "next" at the bottom (while preserving the already configured servers). The program will go through the checks for the IMAP and SMTP settings, and then will offer you:
"Your name (for outgoing messages)" .
Here you enter your name as you want that to appear.
Then click on "Save".
(And just in case, "Account name" on this screen - is how this account shows up in the accounts list.)
Also, I have the paid (Aquamail Pro) version (it is only $5), and that allows me to have multiple identities for the same account, where I can configure different appearances of:
1) name 2) account address [this is useful for when you have role-based alias addresses for the same accounts] 3) different outgoing (SMTP) server ...
This can be configured by long-press on the account -> Identities.
HTH.