What is the name of this transform similar to the Radon transform?
This is a simple Cartesian to Polar coordinates transformation. Instead of expressing the position of a pixel using $(x,y)$ you are expressing it using $(r, θ)$ where $r$ is distance from the centre $(x_0,y_0)$ and $θ$ is angle.

The images are exactly the same, wherever they are definable, but the "unrolling" results from still using $(x,y)$ to depict $(r,θ)$.

For more information, please see this and this.