Is this a privacy issue?

Dear nurses, I appreciate your input on my paranoid Hipaa questions. I have another: I'm a non-medical staff with regular patient contact in a healthcare facility. Recently, a patient who has some confusion wanted to contact someone in their "circle" of people. This person had a list of names and numbers that family had given them so they could reach them when needed. Because this person is somewhat challenged physically, I offered to dial the number for them, and then handed them the phone. I was 99.9% sure that I'd dialed the number correctly, but I could hear the voice on the other end say that it was the wrong number. The patient didn't accept this at first, and went on to state their name (first and last) to the person and another family member's full name. The patient didn't say that they were a patient at the facility, but in today's caller-ID reality, I'm rather sure the person on the other end would see the name of our facility. So, given that the patient didn't say "Hello, I'm (full name) and I'm a patient at this facility", even though they stated their full name, would this be a privacy violation since they didn't speak to the person they intended to reach. Furthermore, am I at fault since I was the one who dialed the number?