You can easily add your logo to this simple coaster design in Blender.

• Download coaster STL and import to Blender
• Import your logo as SVG into blender 
  • Join all curves into one curve 
    • A, Control J
• Convert SVG to STL
• Extrude STL z to ~5mm
• Scale Logo STL to appropriate size (Coaster should be ~100 mm diameter)
• Use Bool Tool Union to merge your Logo with Coaster
  • Embed so that your logo z position is halfway above inner circle (~2.5mm)
• Export STL and slice using your preferred method

How to improve:

• Bevel the inner coaster for round edges
• Change depth and other dimensions
• Make sure your SVG has only necessary vertices
• Print in different colors