"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.