They left India a long time ago, so long they don't actually know when, why or from where, just somewhere in the Indian subcontinent based on their language (bears features from central India as well as northern Pakistan) and cultural beliefs when they were first recorded in Europe in medieval times. They were often associated with Egypt in the minds of Europeans, hence the term Gypsies.

The Roma name is a coincidence, but Romania has long had a high population of them, so it probably reinforced the name.