Not sure I understand as that’s all they’re identified by until Poe gives Finn his name? I can see how initially it may feel out of place for him to just pull it out of the air but the way he pauses alludes to some use of the force that gives him this information. Anyway, it’s exclusion doesn’t effect the main plot but I feel it might hurt his character development a little as its another scene that’s helping establish his power with the force for the audience and as I said earlier, draws some parallels with DV which is part of the overall story.
It just seems weird to me for the big bad villain to even be concerned with a serial number. To him, I’d expect Finn to be “that one trooper.” I’ll probably undo the change, though, leaving it just about SKB and R2.