stamping on a model

I’m new to blender and I need to stamp my model with a badge I did this in sketchup by intersecting faces then just filling it in on where the badge intersected the face was and I’m trying to figure out how to stamp my badge on blender and if needed I can recreate the badge but I don’t know you to stamp it

I’m unsure of what you mean by stamping, but without seeing screenshots, maybe you would like to use booleans, so here’s an example :
i have 2 separate objects, i made sure their normals are correct before continuing.

Intersecting both

And using the booleans operation modifier on the sphere, set to “Difference”

Applying it , deleting the original text object object

Adding an Edge Split modifier to the sphere to make the edge hard visually , getting rid of the bad lighting (booleans generate some messy geometry that can lead into some not so good shading with the light)

not quite because I want it to be like a painting on my model and I use a badge same concept as the one you use