Dhampirs wear two categories of tattoos. The first is a Promise Mark, to prove they successfully finished guardian training. The second type of tattoo is called a Molnija Mark and a guardian gets the mark added to her skin every time she kills a Strigoi.
The Zvezda Mark: The Zvezda mark (battle mark) is given to guardians who have killed many Strigoi. Rose receives her zvezda mark in Shadow Kiss after battling the Strigoi who entered the Academy and kidnapped many of the guardians and Moroi.