You may already be happy with the characters that were introduced in the first book of Fantastic Beasts and Where to Find Them but just like in the Harry Potter series, there will be more characters that you will learn about as they can be vital to the turn of the story. You can familiarize yourself with Leta Lestrange.
She seems to be Newt’s girlfriend but according to the book, she may be engaged to Newt’s older brother. An unidentified Maledictus will be the best friend of Credence and she is the person that he will get to rely on in an unfamiliar place. Torquil Travers is known to be purist. He is also a lead auror.