Text fields can auto-enter the current user's account name at the time a new record is created. Thus, if the "owner" of a record is also it's creator, you can simply create a new record.
To set up a value list of account names is a bit more work as there is no automatic way to get a value list of accounts out of manage security. You'd need to set up such a value list either as a custom values value list or by creating a table of users with one record for each user that could then serve as the source of values for such a value list.
And once you have records labeled with the account names of the person that "owns" them, see "Editing record access privileges" in FileMaker Help and check out this particular sub section: "Entering a formula for limiting access on a record-by-record basis" for a description of how to set permissions such that different users have access to different sets of records in the same table.
That's great thanks, that's what I've done right now and seems to be fine. I just wanted to make sure I wasn't doing it wrong. Thanks!