Sorry, don't have a form but can maybe provide some info. From the US FDA perspective,
820.200 applies and requires that information captured from servicing includes:
(1) The name of the device serviced;
(2) Any unique device identifier (UDI) or universal product code (UPC), and any other device identification(s) and control number(s) used;
(3) The date of service;
(4) The individual(s) servicing the device;
(5) The service performed; and
(6) The test and inspection data.
From a 13485 perspective, the :2016 version states that the manufacturer just maintains records of service activities with no specific requirements for content.
As you can see, there are no specific requirements for signatures. I've frequently seen that companies generally require that the record includes a signature just to reinforce data integrity.
Do note that there are other considerations for service activities that are outlined in the respective regulation / standard. For both, this includes that the service procedures themselves be documented and that information from service activities is reviewed for potential complaint and for potential improvements.