do you have any about the reason why they picked 34? and 3b?
The "34" was a designation the US government established for the military engine at the time the engine was designed and selected, the TF34.
The "3B" relates to the commercial CF34 engine. The sequence started with the original "3A" engine which powered the Challenger 601 business jet and the Canadair Regional jet.
The "3B" designation indicates a change in the engine. It was a variation, an improvement over the "3A", offering an ~3% lower specific fuel consumption resulting in an improved 5-7% operating range for the newer Challenger 604 plus a higher climb rate and shorter high/hot field takeoff capability.