By update username, do you mean re-assign? If so, using the REST API you could use the claim task API 
Edit: Just noticed there is a field called user name. You could update the process variable using the variable REST API . Given there is a form, you could change the value via the form unless the field is read only. If you update via the form, the form SDK takes care of updating the process varaible.
 https://docs.camunda.org/manual/7.7/reference/rest/task/post-claim/ https://docs.camunda.org/manual/7.7/reference/rest/task/variables/post-modify-task-variables/
API completely solved my problem. Thank you.