If you have formed a civil partnership then your civil partnership certificate will be sufficient documentary evidence in order to change your surname to that or your partners.
If you wish to form a double-barrelled surname then your civil partnership certificate will also be accepted by all UK Government organisations i.e. the Passport Office but other institutions i.e. banks may require a Change of Name Deed Poll for this purpose, if in doubt please contact the company in question.
If two women form a civil partnership and one or both of them would like to change there titles to Mrs then this can be done via a Change of Name Deed Poll.