Add two fields to registration for in Wordpress

1.) Two fields need to be added to my registration form on Wordpress through child theme. 2.) Display input on the users public profile under name. The registration form is through a custom plugin and not a form plugin. I already have the form field built and ready to be inserted. I do not want any plugins installs and this should be a simple hook on the [login to view URL] file of child theme. The website is [login to view URL] <div class="row"> <div class="col-sm-6"> <div class="form-group has-feedback"> <label for="reg_branch" class="bold"><?php esc_html_e( 'Branch of Service *', 'adifier' ) ?> </label> <select class="form-control" id="reg_branch" name="branch_service"> <option>Navy</option> <option>Marine Corps</option> <option>Army</option> <option>Air Force</option> <option>Coast Guard</option> <option>National Guard</option> </select> </div> </div> <div class="col-sm-6"> <div class="form-group has-feedback"> <label for="reg_status" class="bold"><?php esc_html_e( 'Status *', 'adifier' ) ?></label> <select class="form-control" id="reg_status" name="reg_status"> <option>Active</option> <option>Reserves</option> <option>Retired</option> <option>Discharged</option> <option>Disabled</option> <option>Dependent</option> </select> </div> </div>