Is the name being removed earning an income? If so and even maybe if not then there may be underwriting considerations that could mean it has to go the same route as a new mortgage.
In theory most banks can just remove a name but in practice it depends on the systems and the policies of the banks, end result is much the same unless underwriting is needed. For example bank I am familiar with always had individual customer numbers for customers and main earner on mortgage was first named so mortgage was under that number. To remove the main customer meant setting up a new mortgage, to remove the joint meant just removing the second name, assuming there were no other changes re underwriting etc, for example very straightforward in case of death of joint account holder.
However some banks set up totally new account with same details etc so it's kind of hard to say what system your bank uses. Also if the joint is being removed from deeds then that's another issue regardless of bank.
