Fields that take a default value only

I want to have a contact form that is on a “members only” page. Therefore the user is necessarily logged into my site and I already know his/her name, email address etc.

Q: How can I ensure that the output email is necessarily sent to the user’s default name & email address?

Ideally I would like to have the user’s name and email absent from my contact form. However, if I leave these off then I don’t see how I can use them as email tags.
My next approach would be to have these fields on the form but have them default to the known user name and email. BUT how do I avoid the user being able to (accidentally) change these fields?

https://wordpress.org/plugins/contact-form-7/