Some models have a letter and a number (J - 201, K - 231)
Some have a number and a name (252 - Missile, 262 - Rocket)
Some have a letter and a name (M - Bravo, R - Ovation, S - Eagle)
All Mooneys, except for the original M20 and the M22, have at least one letter (the Acclaim is the only one I know of to have two letters, the TN). Most, but not all, have a name as well; for some of those, the "name" is a number.
The J is also known as (depending on when it was made, and what options were installed) the 201, the 205, the Advanced Trainer, and probably other things I've forgotten. When Rocket Engineering bolts an IO-550 onto it, it becomes the Missile.
The K, from the factory, was either the 231, 252, or the Encore (most notable differences between these models are the engines--all are TSIO-360s, but the 231 was either a -GB or -LB, the 252 was a -MB, and the Encore was a -SB). When ModWorks bolts the engine from a 252 onto a 231, it becomes a 262. When Rocket Engineering bolts a TSIO-520 onto any of the K models, it becomes a Rocket (though I've never heard of a Rocket conversion being done on an Encore, and I understand they're pretty rare on 252s).
Missile, Rocket, and 262 are aftermarket names, not "official" Mooney designations.