Adam is a person's name. So, can I say: Adams are four brothers. In my language it's possible. We always make plural of people's names.
In English, in order to say that phrase you would pluralize the name and add an article.
The Adams are four brothers.
There is more information on how to pluralize a name on this website.
Here is an example of pluralizing a name and using an article found in The New York Times:
The Obamas were at the University of Arizona
If you were saying that about only one person, you would say:
Obama was at the University of Arizona.
It's also worth noting that saying "The Adams are four brothers" still sounds somewhat unnatural because it implies that "four brothers" make up all of the Adams. It would sound more natural to say something like:
There are four brothers in the Adam family.
I would add a final note that "Adams" is a common last name (surname or family name) in English. "Adam" is more common as a first name.
If you were pluralizing "Adams" you would say "Adamses."
John Quincy Adams and John Adams were both Presidents of the United States. The Adamses had different approaches to leading the country.