The Duke and Duchess of Sussex have named their newborn son Archie Harrison Mountbatten‑Windsor.

Introducing him to the cameras this morning, Meghan Markle said Archie has been a dream.
The announcement came after the Queen and Duke of Edinburgh met their eighth and newest great‑grandchild for the first time at Windsor Castle.

By deciding to call their son Archie Harrison Mountbatten‑Windsor, Harry and Meghan have chosen not to use a title for their first born.
As the first born son of a duke, Archie could have become Earl of Dumbarton ‑ one of Harry's subsidiary titles ‑ or have been Lord Archie Mountbatten‑Windsor, but instead he will simply be Master Archie Mountbatten‑Windsor.
BBC reports it is a "strong indication that they don't want to bring him up as a formal 'royal'".
[Source: BBC]