The process for people wishing to change their gender on their bank account has also been simplified, the bank said in a statement on Transgender Day of Visibility.
Instead of using the conventional honorifics Mr, Mrs or Ms, customers can choose from 10 gender neutral titles - Mx, Ind, M, Mre, Msr, Myr, Pr, Sai, Ser and Misc.
"Gender neutral titles allow people who don't identify as a particular gender, or who don't want to be identified by gender, to choose the title that works for them," the bank said in a statement.
The titles, available to its high street customers in Britain, will be applied across their account including bank cards and correspondence. Training is to be given to all UK branch and contact centre staff.
Customers who are transitioning can now change their gender on their account by taking a passport, driving license or birth certificate that supports the change of gender into a branch.
Stuart Barette, trans lead of HSBC's UK Pride Network, which advised on the new services, recalled how he was "terrified" the day he went into his branch in order to change his name and gender.
"Coming out to anyone is difficult, as you don't know how people are going to react," Barette said in a statement.
"That's why the changes we've been making are so important, so that our trans customers can feel confident that they're going to have a good experience and be speaking with someone who has been trained to better understand them."
The titles are also being introduced for people who do not feel their gender to be that of a woman or man.
Ind is an abbreviation of individual, Mre for mystery, Msr is a combination of Miss and Sir, Pr an abbreviation of person.
International Transgender Day of Visibility marked on March 31 aims to raise awareness of discrimination faced by transgender people.