Hi Mike thanks for posting in the Lucid Community! To clarify are you referring to names as they appear alongisde comments in the comment panel? In the example below this is the "You" label on a comment I've created.

If so it's unfortunately not possible to disable this. However if you invite others to your board as Guest Collaborators they will be assigned a random name which will prevent association of edits to the board including comments with any specific person. To learn more take a look at the linked article from the Lucidspark Help Center.
If you'd like to see support in the future for disabling names on comments our development team would love to learn more about your use case via the Product Feedback space in this community. They use feedback submitted here to prioritize improvements to Lucidspark! Thanks for your feedback - let me know if you have any additional questions below!