Introdece yourself

When you meet someone for the first time, you have to itroduce yourself.

hajimemashite : how do you do (learn it as a phrase)
namae : name
to moushimasu : (literaly means " I say...", but usually means "is")

Hajimemashite; how do you do : How do you do.
Watashino namae wa Suzuki to moushimasu. : my, name , Suzuki, is. : My name is Suzuki.

It si OK to say " Watashino namae wa Suzuki desu(is)."

Usually, "you" or " I " as a subject is omitted, then, you can say like this ;
Suzuki to moushimasu. : Suzuki, is : ( I am ) Suzuki. / (My name) Suzuki.

Remember that there are many cases in which a subject of the sentense is omitted.
You should concentrate on listening ordinary nouns and proper nouns but " watashi ( I )" as a subject. Personal pronouns are not so important in our conversation because you can imagine them.