If you find a mistake, contact
BRPError@homeoffice.gsi.gov.uk within 10 working days of receiving your permit providing full name, date of birth, nationality, case reference number, contact telephone number and details of what is wrong with BRP.
You can also send details to
Returns Unit
P O Box 163
Bristol BS20 1AB
To be honest, signatures are barely visible clearly on the BRP. So not sure minor changes in the signature on BRP should really be a cause of concern. They already have your biometrics which are unique to every individual so I guess signatures are only supplementary information in addition to biometric details.