HMRC and your employer are separate updates
Your employer keeps its own payroll record and reports your pay to HMRC. It’s tempting to assume that updating HR is enough, but HMRC expects you to report your change of details yourself, and your employer to update payroll. Do both, around the same time, so your payslips and your tax record show the same name.
Pension providers work the same way. A workplace or private pension keeps its own records, so tell it directly, or check whether your employer passes the update on. Our guide to changing your name with your employer and payroll covers the HR side.