Is 'Alphabet' called alphabet because the first letters of Greek language are alpha and beta?

Yes. The reason that the alphabet is called the alphabet is that the Greek alphabet and communication system is one of the first. The first two letters of the Greek alphabet are alpha and beta. It is these two words which give way to alphabet. The word alphabet first made its apperance during the Middle English era where it drew the word from Late Latin and the word alphabetum. The first two letters in the Phonecian alphabet are aleph and bet which also lends influence to the word alphabet.

Scientists believe that the alphabet gets its earliest influence from the ancient Egyptians and their complex method of writing and communicating. This original alphabet would be the reference and influence that would develop the alphabet for all of the languages that have ever been spoken on Earth. These early alphabet scripts and writings would set the wheels turning for the way that people are able to communicate to this very day. One can easily say that the alphabet is the most influentual instrument of all of history.