To actually try and answer the question, in some cases yes, in others no.
Pratt & Whitney currently use a system where the last two digits represent the rated TO thrust, so a PW4056 produces 56,000 lb static thrust at TO. The generic engine name being the PW4000. The PW2037 was a 37,000 lb engine and so on. PW turboprops have a similar system, but in terms of shaft horsepower. So a PW120 nominally produces 2000 shp at TO.
Other manufacturers do this in a more approximate way.
For the GE CF6, the dash number came to represent the upper range of thrust for the engine family, so the CF6-50 is a 50,000 lb class engine. The CF6-80 was designed to be grow to around 75,000 lb, so it starts to get approximate. There was a CF6-32 projected for the 757 so the pattern is there.
The 90 in GE90 originally meant the thrust class, but now GE90 is the generic engine name, with a dash number representing thrust class.
RR seem to have adopted a similar system to PW with the Trent, in that the last two digits represent something approximating to the TO static thrust. The first digit or digits representing a family of similar engine ratings. The Trent 553, 556 and 560 are basically the same engine, but with different thrust limits.
Before that, RB211 dash numbers appeared to sometimes relate to approximate thrust in different ways. For example the RB211-
524 originally was a 50-53,000 lb engine. However as it's thrust grew, the number remained the same. The -5
35 was originally a 37,000 lb thrust engine. Again it didn't change as the engine thrust grew.
As for the CFM56, who knows what the 56 represents. It may simply have been a number that sounded good in English and French.
