By "sanitise" what's really meant is usually "escape". User typed their display name as <script>. You want the screen to say their display name, which is <script>. Therefore you send <script>. That's not their display name - that's just what you write in HTML to get their display name to appear on the screen. You shouldn't store it in the database in the display_name column.
Agreed. The codebase I'm thinking of was html encoding stuff before storing it, then when they needed to e.g. send an SMS, trying to remember to decode. Terrible.