As an aspect of 'immersion', I'd like to be able to name any unit as soon as it is built or bought, and have a good long (25+ characters) field for unit names, to give maximum flexibility to the naming.
No format for the name, either: if I want to name them using all numbers, or letters, or a combination - my choice.
So, I could have a Renaissance Russian unit named the Preobrazhenskii Guards Infantry, or a British 2nd North British Dragoons cavalry unit.
Or, which I've managed to do by judicious promotions and naming in a single game, have a recreation of the British 'I' Class capital ships. Historically, they were WWI Battlecruisers with names like HMS Inflexible, HMS Indomitable, etc. Mine were the HMS Insipid, HMS Inconceivable and HMS Incontinent, which adds a note of whimsy when they are pounding Pedro's capital into finely-ground rubble.
AND we should be allowed to Change names: say, whenever a unit gets Promoted or Upgraded, or destroys an enemy unit in battle. That way, we could add 'battle honors' or descriptive titles to unit.
For instance (and I use a lot of Russian examples, because I've been studying the Russian/Soviet military for decades) after they take the enemy city of Orleans, I could rename the Preobrazhenskii Guards as the "1st Order of St George Orleanskii Guards Infantry"
Or I could give units 'nicknames' based on their performance: a unit that destroys several enemy unit attacking it should get the title: "Iron Brigade" (or Division) - every army should have an Iron something to designate a particularly tough unit: historically, the French Army had the 11th Iron Division, the US Army had the 1st Iron Brigade in the Civil War, and the Soviet Army had the 24th Zheleznaya (Iron) Division in WWII.
We need something like this in the game to 'tone down' the unrelieved mass of mathematics that governs all combat now . . .