It's fine, Zoltan. The noun 'Facebook' is used attributively to modify another noun in the same way as an adjective does.
Compare 'police station', 'school entrance', 'car door', 'Google search', 'Mercedes saloon' etc.
I changed your title, Not sure about spelling (S-V-O sentence), as it had nothing to do with your question.
('We became friends on Facebook' is fine, too.)
Student or Learner