The processing times seem to vary quite a bit, even for applicants with similar profiles. It’s interesting to see how different everyone's timeline can be. Hopefully, more 2023 applicants will start receiving positive updates soon.
You’ll need to apply for a PR card amendment/correction through IRCC, not BLS Brampton. Usually they ask for your passport copy, PR card, and a letter explaining the name mismatch. It’s best to contact IRCC or check their official correction process before applying for citizenship.
If your application was received on 17th Jan, it may not be included in the batch processed by 15th Jan. You should check the official portal or contact support for the latest status updates specific to your case.