Apple's Mail.app is obtuse sometimes, but at least it has nice e-mail alias support, as offered by e.g. Fastmail (see here).

  1. Settings => Accounts => the account you want.
  2. Account Information => Email Address.
  3. Edit e-mail addresses. Add the aliases you need.

The added aliases will show up as available senders when composing.

Also within Settings => Accounts the Server settings appear to allow switching of SMTP servers. Neat!