Princeps Senatus, would that be the speaker of the house?
More likely that the President would be the Princeps Senatus, and thus speaker of the Senate at the same time.
Does anybody have any ideas on alternate names for positions in the US Government, such as Attorney General or referring to those in charge of US departments as secretaries?
I think you could name the whole government after Roman examples.
President: Princeps (or [First] Consul); maybe even
Praetor Maximus
Vice President: (Second) Consul
Secretaries: Praetors
Secretary of State: that's hard. Maybe
fetial?
Secretary of the Treasury: Quaestor
Secretary of War: Consul
Attorney General: Praetor
Postmaster General: Aedile
Senate: Senate
Speaker of the Senate: Princeps Senatus
House: Comitia or Tribunate (because of the People's Tribunes)
Speaker of the House: Tribune
Members of the SCOTUS: Ephors (the Ephors enforced the Law in Sparta) or Censors
Governors: Proconsuls
Governors of territories: Propraetors
Mayor: Duumvir