Your systems call your patients, clients, and customers by a name they no longer use, but is difficult for them to change or they are in the process of changing.
Calling someone by the incorrect name can inadverntenly expose their gender status. Exposing someone's trans status without permission can get them fired from their job, renounced by their family, or threatened by strangers.
Calling someone by the incorrect name is also seen as an insult and belittlting, even when done by accident or mis-design. You are delegitimizing that person.
By making sure your systems provide an affordance such that your clients, patients, or customers can be called by the name they wish to be called, even if it doesn't match what's on their state-issued ID. And not just on the web and native apps, but on the phone, in correspondence, texts, and in person.
People will be reluctant to use your service, contact your staff, or come in for care. If it's about a delinquent account, it will go into collections. If they are a patient, they will stop following up on care. The federal goverment is scruitinizing this area, so you could find yourself in violation of EEOC and Title IX.