Unfortunately, one of the advantages of the telephone serves as a disadvantage when it comes to phone introductions: the inability to see the other party’s face. This means your entire first impression falls solely on your words and tone. Accordingly, when introducing yourself over the phone it is important to create a presentation that is clear and to convey a friendly demeanor. You must give the person on the other end of the phone an idea as to why you are calling and create a desire to continue the conversation.
Identify yourself at the onset of the call. For example, you might say “Hello, my name is (your name).” When introducing yourself on a business call, use both your first and last name and professional title, such as doctor or reverend, if it is related to the purpose of the call. When you are introducing yourself for a personal call, it is fine to use just your first name.
Ask to speak with the person you are calling by saying, “May I speak with (person’s name)?” Do not assume you are speaking with the correct person. If the person has already identified himself upon answering the phone, confirm that you heard the correct name before continuing. Listen carefully to how the person introduces himself, and repeat his name exactly as spoken including any titles such as Dr., Mr., or Mrs. Introduce yourself again when the person you are calling comes to the phone, if he is someone other than the person who answered the phone.
State the purpose of your call. Include the company or organization affiliation when applicable. For example, say something like “I am calling on behalf of (company/organization name) in regard to (reason for the call).” When making a personal call to someone you recently met, begin the conversation by reminding the person when and where you met: “We met Wednesday at the park.”
TL;DR (Too Long; Didn't Read)
Speak clearly and slowly and at a moderate volume when introducing yourself. Smile while talking. Even though the person on the other end of the line doesn't see you smile, the act of doing so puts a smile in your voice. You will sound happy and friendly.
Listen carefully to the person who answers the phone. If he answers the phone by stating his name such as, “Hello, (name) speaking,” make sure to use the person’s name in your introduction, “Hello (repeat name). My name is (your name).” Then ask the person whether he has a moment to speak with you. Do not assume the person wants to speak with you at that time just because he answered the phone.