Being transsexual presents no problem as far as banks or building societies are concerned. They will apply exactly the same criteria in the case of credit assessment as for anyone else.
The bank will change your name as a matter of course once it has received a certified copy of your statutory declaration. The bank will also require a signature card with your new signature or in the case of a second account the signature which you will use for the operation of that account.
Again altering details on these and requesting new ones will present no problems. Simply send a covering letter to the credit card company together with a copy of your statutory declaration requesting a change in your name and requesting that new cards be issued in that name.
Do however watch out for the fact that certain credit card companies utilise gender checking as a form of security. On some credit cards the gender may be stated in which case it is easy to see the alteration but on some others such as Barclaycard there is no gender indicator as there are only initials. The use of initials is a deliberate part of the security system in that if your card is ever checked for any reason then the first thing the shop assistant is asked of the cardholder is the gender of the cardholder. Therefore make sure that the credit card is tied to an account in your preferred name.