J.K. Rowling was awarded an OBE by Queen Elizabeth II in 2001.
OBE stands for Officer of the Order of the British Empire. Rowling received the honour in the 2001 Queen’s Birthday Honours for services to children’s literature. At the time, the Harry Potter books had become an international publishing phenomenon, with readers in many countries.
An OBE is one rank within the Order of the British Empire. It is below a CBE and above an MBE. Receiving an OBE does not make its holder a knight or dame, so “Dame Rowling” would not be the correct title resulting from this honour.
Rowling received other recognition later, including the Hans Christian Andersen Literature Award in 2010 and a Companion of Honour appointment in 2017. Those distinctions are separate from the OBE she received in 2001.