A name change by deed poll does not affect your pension entitlement in any way. Your pension pot, employer contributions, state pension entitlement, and any defined benefit scheme rights all remain exactly as they were. What you need to update is the name on your pension account records, so that correspondence, annual statements, and eventual payments are issued in your correct name.
For workplace pensions, the pension provider is often different from your employer — they are typically managed by a third party such as Nest, Legal & General, Aviva, or Scottish Widows. When you change your name with your employer's HR team, this update may not automatically flow through to the pension provider. Contact your pension provider directly with a certified copy of your deed poll to update their records. Your employer can usually give you the contact details for the pension scheme administrator.
For private pensions or self-invested personal pensions (SIPPs), contact the provider directly. For the State Pension, your record is tied to your National Insurance number and is maintained by HMRC and DWP — updating your NI record (see our guide on National Insurance updates) should flow through to the State Pension system, but it is worth verifying with DWP if you are close to retirement age.