Yes, you can add however many names you like to your name. You need to get a deed poll. However, you should be aware that HM Passport Office can only print a maximum of 30 characters as your Christian name (and this includes your middle names), and a maximum of 30 characters as your surname.
If your new Christian name and middle names exceed the limit, you should request that they add an abbreviated form in the main part of your new passport, and that they print the names in their entirety on the observations page.
