Users see previous display name:
Changing your profile name doesn't change the display name for users who already have your contact on FYI. FYI users see the display name you had when they added your contact, therefore they don't see any changes to your display name. To fix this, other users have to change your contact name locally on their device.
Users see different display name:
If the display name has changed into something completely different for another user, they can check their local phone contacts. They could have added your phone number to another FYI user's contact. This causes your display name to be that contact name instead.
To change your display name follow this guide.