Changing your name after a civil partnership works in much the same way as after a marriage, but with one important practical difference: not all organisations currently accept a civil partnership certificate as evidence of a name change in the same way they accept a marriage certificate. Some government departments and private organisations have updated their processes; others still have staff trained primarily around marriage certificates. A deed poll avoids this ambiguity entirely by giving you a single, universally recognised document regardless of the organisation.
If you want to take your partner's surname after a civil partnership, a deed poll stating your former name and your new name is the clearest evidence to present. Unlike a marriage certificate, which implies a specific naming convention, a deed poll covers any change: taking your partner's name, creating a double-barrelled name, combining elements of both surnames, or adopting a completely new shared name. Both partners can each use their own deed poll to adopt the same new name.
The Passport Office, DVLA, HMRC, and most banks have updated their processes to treat civil partnerships equivalently to marriages. However, in practice, having a deed poll ensures you do not encounter delays at organisations whose staff are less familiar with civil partnership certificates. The process of signing and using the deed poll is identical to any other name change.