My name is...

Давайте познакомимся! 
Меня зовут Таня.
Как вас зовут? 

Learn how to tell you name:
Меня зовут ...

Learn how to ask someones name:
Как вас зовут? (formal)
Как тебя зовут? (informal, especially addressing children)
Как его зовут?
Как ее зовут?

Every Russian name consists of three names: a first (given) name, a patronymic name and a surname:First (Given)

Vladimir   Vladimirovich          Putin
Lev          Nikolaevich             Tolstoy
Fedor       Mikhailovich           Dostoevsky

First name

The first name is given by parents shortly afer the child's birth. Accordingly to Russian laws child can change the name after majority. The first name is the main name of Russian people. Most of Russian names have a variety of forms. For example, name Mikhail. The full form Mikhail is used in formal relationships, in official documents (passport, birth certificate, contracts). The short name Misha is used by friends and family members. Affectionate form Mishenka, Mishunya is used by parents, grandparents. And rude form Mishka is impolite.

Patronymic name

Russian patronymic name is derived from father's name according to rule:
Russian male patronymic name forms by adding ending -evich, -ovich. (Nikolaevich, Mikhailovich).
For example, Lev Nikolaevich Tolstoy. Tha name of Lev Tolstoy's father was Nikolay, so the Lev Tolstoy's patronymic name is Nikolaevich.
Russian female patronymic name forms by adding ending -ovna, -evna. (Nikolaevna, Mikhailovna). For example, Raisa Maximovna Gorbacheva. Tha name of Raisa Gorbavheva's father was Maxim, so the Raisa's patronymic name is Maximovna.

Russians used First and Patronymic Name in formal relationships, with unfamiliar people, with doctors, teachers, lecturers, older members of family, directors, leaders and other respected people (ex. Vladimir Vladimirovich, Lev Nikolaevich, Fedor Mikhailovich).

So, As I am a teacher... Меня зовут Татьяна Владимировна