There are 542 surnames belonging to that nationality that we know of.
There is one funny thing about Estonian surnames worth mentioning. The most popular name (according to the censuses anyway) is Ivanov, which clearly has Russian origin. And it is not the only name Russian roots. Up on the list are Smirnov, Vasiliev, Petrov, and so on and on. That is of course the result of Estonia being part of Soviet Union for a number of years and assimilating a great number of people from the nearby areas and from all sorts of military bases there.