WordPress will automatically assign a unique ID to every user on the website. If possible, I'd suggest simply using that auto-generated ID. You can create a dashboard widget that only displays for admin users, and add whatever activity you like. When you display their ID, you can have it output "Member " and pad their WP ID, so it appears like "MEMBER00000001" for the admin, even though the actual ID in the database is simply "1".
Customizing existing user IDs is not advisable, since the user ID field in WordPress's database is "bigint" (i.e. it can only contain numbers, no letters).
If you really want to create your own member ID number in addition to WP's built-in user ID, I'd suggest adding custom user meta. You could create your own plugin that automatically adds your desired unique ID every time. You could say: if there are no existing users, set the first one to "MEMBER0000001", but if there are existing users, get the latest custom ID and add 1 to the number portion, then concatenate the string "MEMBER" with the new number.
There are also a number of user meta / registration plugins available. You can try some of those out and see whether they allow you to add this extra field in a way that's invisible to the user (since I assume you don't want users to type in their own ID).