I think you might be looking for some variant of a double try square.
A try square is:
a woodworking or a metal working tool used for marking and measuring a piece of wood. The square refers to the tool's primary use of measuring the accuracy of a right angle (90 degrees); to try a surface is to check its straightness or correspondence to an adjoining surface.
A traditional try square has a broad blade made of steel that is riveted to a wooden handle or "stock". The inside of the wooden stock usually has a brass strip fixed to it to reduce wear. Some blades also have graduations for measurement. Modern try squares may be all-metal, with stocks that are either die-cast or extruded.
I haven't been able to find a picture of a double try square, with two L-shapes linked together, as you're looking for, but here are various images of single try squares taken from here:
The second of these is called a framing square and the third a bevel square.
A machinist square is the all-metal equivalent of a try square. From Wikipedia:
A machinist square or engineer's square is the metalworkers' equivalent of a try square. It consists of a steel blade inserted and either welded or pinned into a heavier body at an angle of 90°.
More pictures, from various sources:
Hopefully at least some of these look similar to what you're hunting for, or at worst will give you some helpful search terms!