And for each US domestic rotation each individual aircraft was reregistered onto the US N-register, and then back onto the UK or French register for the Atlantic crossing.
At that time only N-reg aircraft were pemitted to operate internal commercial US flights.
To simplify the process the BA Concordes were allocated unique-for-the-UK alpha-numeric registrations which could have their 'G-' prefix hidden by speed-tape:
Here's a link to an old Braniff schedule showing the Concorde as a route out of DFW...
This segment was sub-sonic, though.