They can keep the name sub class no problem, and as most subclasses at 3rd level gets several things, some can be split between 1st and 3rd level.
I.E. Scout rogue can get Nature and Survival proficiency at 1st level with reaction movement at 2nd level and expertise at those skills at 3rd level.
My point was that some features are linked together in subclasses when there really should be 2 choices like how Warlock work.
What if my scout isn't a Nature scout but an Urban Military scout or an Organized Crime Lookout?
Like the Tempest Cleric is a Heavy Cleric. But you really should be able to choose if you want to be Thor (Heavy armror, martial weapons, Divine Strike) or Storm (Bonus Cantrip. Potent Spellcasting).
Monks should be able to choose Dex based Martial Arts, Str based Brawling, or Wis based elementalism.
Wizards should be able to choose Scholary, Bladesinger, War, or Witchy wizard at level 2.
It also lets every class get specialized and complex at the same pace.