"I am Zsuzsa."
This is what immediately came to my mind: http://magyar-irodalom.elte.hu/sulinet/igyjo/setup/portrek/ady/semutod.htm
The second verse technically starts with the construction you want to use.
You shouldn't say "Vagyok Zsuzsa.", though. This phrase is somewhat idiomatic. In practice "Zsuzsa vagyok." is used every single time.
The word order is not free, it is just more flexible than English word order, because there is conjugation. The words themselves carry much of the information that is only implied by word order in English. But still, there are rules for word order.