Removing a middle name from a British passport
The Passport Office’s small-forename-changes guidance allows removal of middle names and changes to the order of forenames using two documents showing the new name. Examples include a driving licence or bank statement. Follow the application’s exact instructions. HM Passport Office: small changes to forenames
For a change across all your records, check the evidence needed by your bank, employer and any foreign authority too. A deed poll can provide a clear record of the complete name you have chosen.