I would recommend using Adobe Illustrator or Photoshop. There is more information on logo design on Company Logos.
How Do You Digitize Logos?
Digitizing something means to convert a digital graphic file into a stitching file for embroidery. Is that what you mean?
Adobe Illustrator does it quite well - you scan the logo, import the scanned (raster) image into AI, then ask it to "trace" it and you end up with a vector image you can tidy up then scale to any size, etc.