A CNC embroidery machine is a great option for making custom tags for fabric things you make yourself.
I decided to make tags with the logo of my family's business, Wildwood Adventure outfitters.
-ribbon (the width and twice the length of the tag you want)
-a CNC embroidery machine
-a vector image of your logo
-a bigger piece of stabilizing fabric
This tutorial is for the Singer Futura 250.
Step 1: Get your logo
For best results, you need a logo image that has large blocks of color. These will be easy for your machine to separate and sew.
Step 2: Import into Futura
Use AutoPunch to make your image into a stitch pattern.
Step 3: Prepare Fabric
Stretch your ribbon across something stabilizing that you will be able to tear away after sewing. I used regular printer paper, and it worked okay.
Step 4: Sew and enjoy!
My thread tensions were a bit off, but the idea stands. Best if your logo doesn't have too much detail.