Yes, create a dropdown with each username that a form submitter could choose, then use that drop down variable in the Assigned To part of the user task. Based on how you've set up your users, you may need to try usernames or email addresses.

You can set up the drop down field to "Assign values to choices". That way you can put someone's "friendly" name in the choice box for display, and fill their username/email in the values section.