Is burnt milk that sticks to a pan something used in cooking ever? Does it have a name?
Short answers (in Indian languages): Thirattu paal (in Tamil); Doodh peda or Khoya (in Hindi/northern dialects).

If you mean you just boiled and reduced the milk to its minimum volume, that is a common recipe for a "milk sweet" in many parts of India, to my knowledge. In south india, in the state of Tamil Nadu, it is called 'Thirattu paal'. That just loosely translates to 'stirred milk' where paal definitely stands for milk. 

In the northern regions of india, it is an intermediary to "doodh peda" where doodh means milk and I dont know what peda means. Maybe it means "soft block".

Here's is one 'recipe` that calls for a low heat simmer, so things don't burn unless your vessel is thin bottomed. Usually heavy bottom vessels are used for low heat stirred sweet recipes with milk. You can add small amount of sugar, grated vanilla or cardamom powder etc to flavor it additionally.