Great link for a demonstration with a custom stamp for the side of a mug. See the process first hand with Instagram link.
Cleaning up the bottoms of cups and mugs to a glass smooth finish. Polishing the bottoms. The bottom of the form should be finished in a professional manner. This process is easy and provides a glass finish to the bottom of a ceramic form. And it is safe. I use the diamond sanding disc that are designed for smoothing granite from Amazon: https://www.amazon.com/dp/B074Z2V9RN
Here is a quick link to a youtube video on how to make a brass stamp. There are a number of things to consider. Hope this helps.
Video: How to make a stamp.