Yes and no.
[name] to iimasu = is called [name]
For example, if you wanted to say in Japanese "Cat is neko" - you could use that structure: cat wa neko to iimasu = (a) cat is called (a) neko.
You can use the structure to say: My name is Lilli - watashi wa Lilli to iimasu = I am called Lilli.
note: to iimasu -- has other uses you will learn about later. It doesn't always mean "am called".
note also = iimasu, actually means "say", but in this particular structure expresses the idea of "am called" without expressing the individual words.
Another way to say: my name is [name] = namae ga [name] desu = name - (subject marker) [name] is.
namae ga mark desu = my name is Mark (name Mark is).
Expressing MY is unnecessary. namae - is used to refer to your "in" group (you, your friends/family/coworkers etc). onamae (o-, a polite prefix) refers to your "out" group (those outside your "in" group).
Also, if it's clear from context, you can leave out "namae ga". Mark desu = (I) am Mark (Mark am).
So, yes, you can use it to express a person's name or to say what anything is called or referred to as, and you will be understood. It is not, however, literally "my name is".