I'm talking about something in geometry notation and/or drafting, I think. It's the mini right-angle shape you can draw within an angle to indicate that it's ninety degrees.
E.g., the mark denoting angle
There is no name for it. The literal interpretation would be 90 degree angle.
It is a special case of the markers that denote the angle between two rays. For example, you could use an angle arc(shown as theta in your image) and beside it specify that its value is 90. Those two symbols would be equivalent.
After reading the Wikipedia article, it may be necessary to distinguish the 'English' right angle symbol from the 'European' right angle symbol of an arc with a dot. I'm not sure that 'European' is exactly the right word to use, but I wasn't able to turn up any results for that symbol with a search. There is a UNICODE symbol, "right angle with arc": ⊾ but there's no dot there, so I don't think it's the same thing.
Quadrant (n = 4)
The quadrant is 1/4 of a turn, i.e. a right angle. It is the unit used in Euclid's Elements. 1 quad. = 90° = π/2 rad = 1/4 turn = 100 grad. In German the symbol ∟ has been used to denote a quadrant.
–Wiki: Angle (emphasized)
At TEX.SE, they're colloquially called a right angle symbol. In the code however, it's called a right angle quadrant.
Perhaps it is the Unicode character U+221F Right Angle, although a few other mathematical angle characters exist. See http://www.fileformat.info/info/unicode/block/mathematical_operators/images.htm.