The customer has been told your name and they are expecting your call – still it is worth mentioning you received their details from Jim’s on the first call so they can connect you. Sometimes they may have called a few places so this will help them identify you.
If they don’t answer, leave a message and send a backup text saying something like ‘Hi Mary, it’s John from Action Mowing. I received your details from Jim’s. Please call me on 0411111111 to discuss your job.’