Making a recorded message is a simple task that most people don’t give much thought to. I used to leave my name on the recording but only learned that “bad” people can tie the name and phone numbers together and turn you into a potential crime victim. So changed my recording as follows:
“ Hello, I am not available to answer you call at this time. Please leave a detailed message and the time you called after the beep. I will return your call promptly. Thank you “
However, if you are waiting for a call potentially with employment potential, you may want to include you name.