I have never figured out the meaning of the letters and numbers in the RB.211 family of engines. The -22, -535, and -524 series seemed to be named rather randomly. Nevertheless, the letter(s) follow the -524 designation shows a chronological development of this sub-family. The last model in the -524 family has the G/H-T designation, the T stands for Trent because Rolls fitted the Trent 700 core with the -524G/H IP and LP spools.
The Trent family technically speaking is a derivative of the RB.211 family. Thus, one can argue that the RB.211 did finally take on a name of a river in the UK.
The Trent naming scheme follows closely a scheme started by Pratt & Whitney when P&W launched the PW2000. P&W's scheme is very easy to understand. Engines made by P&W Canada have 3 digits. An even first digit means it's a commercial engine, while an odd first digit means it's a military engine. The last two digits are the engine thrust rating in k-lb. Engines made by P&W in the US have 4 digits. Just like the P&WC case, the first digit distinguishes military or commercial engine. The last two digits are also used for the engine thrust ratings in k-lb. The second digit tells you what aircraft company the engine is being used. 0 and 2 are reserved for Boeing applications, 1 is reserved for Airbus applications, 4 was reserved for MDC applications, etc. Thus, PW4084 is a commercial engine (the first 4) to be used on a Boeing aircraft (the 0) with 84 k lb of thrust. Once a while, you will see a letter follows the four digit numbers. I don't know exactly what it means, but I believe it has to do with certain upgrades or FADEC thrust bumps, etc. (I'm not going into the old P&W designations. The JT series designations were rather random, too. I believe the JT stands for Jet engine/Turbofan.)
The Trent bascially follow the same scheme with two exceptions. First, the first digit indicate the thrust range (in Klb, even though Rolls is supposed to use metric units), but Rolls broke that pattern with the Trent 900. Second, the don't have a special digit for applications. At this point, there is no need to, because each Trent sub family is used on one aircraft type only. The last two digits have the exact same meaning as P&W's, i.e., thurst ratings in k-lb.
GE's old designations were rather random, too. The CF6-6, -45, -50, -80A, -80C, and -80E didn't follow logical rule. (BTW, CF stands for Commercial Fans.) However, it is in chronological order. I believe GE did have more meaningful sub-designations when the -80C2 was launched. The letter follows -80C2 is A, B, or D for Airbus, Boeing, or Douglas. The next number indicates the chronological order (and its related thrust) of the engine. Thus, an -80C2B1 would be used on a Boeing aircraft, but there is no way to tell what exactly the thrust rating is. GE roughly followed P&W's scheme when they launched the GE90. The GE90-115B is a 115klb thrust engine to be used on a Boeing application.
The CFM-56 designations are somewhat similar to that of the CF6, except it doesn't use A/B/D to distinguish applications, because each sub-family is being used on one family of aircraft only (except for planes re-engined with the -2). The -3 and -7 are for Boeing applications, the -5A/B/C are for Airbus applications.
Since P&W is a founding member of the V2500, obviously, it also adopted the last-two-digits-for-engine-thrust scheme started by P&W. It also has extra letters/numerics. The V2525-A1 is a 25k-lb thrust engine used on an Airbus aircraft (which is an older model than the -A5). For the MD-90, the V2525-D5 is used. I think it's obvious what the D in "D5" stands for, right?