How to show/hide the title/surname/suffix of my character in the profile & signature?

Go to My characters > Edit > Identity card.

You can choose to show in your profile and signature the title, surname and suffix of your character name.

There is a restriction in the number of letter you can show in your profile/signature names to avoid having them go outside the backgrounds. So it's the reason why sometime you can only show your Name and your Suffix for example.