Does anybody know what the name of this effect is? It is on both the bottom left corner, and the top right of this image, and it seems to be a reflection of some type of light source.
It's an illusion of rounded thickness, created by simulating lights and shadows. The shiny reflection is called a highlight. In Photoshop you can create it with layer style Bevel&Emboss:
The drawn shape is a rounded rectangle. There's also a shadow at the other side, because the light comes from south-west.
You wanted the same to the opposite corner, too. Changing shadow color to white unfortunately doesn't the trick and my antique Photoshop hasn't multiple lights, but I can turn the shadow to another highlight with curves. It's possible because the color is grey:
Grey can be colorized with another adjustment layer above all:
As well there above all could be an image layer with blending mode =Color.
An experienced designer doesn't need effects, in simple cases he draws the highlights and shadows and inserts them with layer blending modes without destroying the drawn shapes.
Real 3D software with proper rendering has best options to make realistic lights and shadows with very little drawing effort.