Don't you mean that you want a Record specific to the user rather than a field specific to the user?
Having a different field for each user as part of the same record is usually a recipe for trouble.
I have a Contacts table/layout. It is universal for all Users. I want to add a Notes Field that is unique for each User on each of the Contact Records in the Contact table. Giving them the ability to make a personal note about the contact. Is that possible?
It's possible, it's just not a good idea. Create one Notes field and put it in a different table. Link that table to the contacts table. Use a portal to list the notes records. A portal filter can limit those visible to those by/for the current user. Access options in Manage | Security could also be set up to achieve the same result and would make sure that no user saw notes that they weren't entitled to see.
And you can, during start up (OnFirstwindowOpen) set a global field the customer table to the user's Account name and then a relationship will limit the notes to just those with the current user's account name and any new notes added to this table via that portal will automatically enter the needed account name.
Note that this sets up the ability to make multiple dated and/or timestamped notes by the same person for one customer. This is more flexible than a single note field where a user makes repeated entries into the same field.
I already have a UserID global variable setup on sign in. So that makes sense. Just filter the portal of notes by UseID. Thank you!