You could setup a rotary fairly simple on an X-Carve. It would only require 3 axis motion to engrave text on the contour of a Pen. You could use a drum switch to change from one axis’s stepper (X) to the rotary stepper.
You would need a way to lock the X axis stepper in place when switching to the rotary stepper and that can be done with the shaft coming out of the back of it. An aluminum disc that locks on the shaft with a set screw and it has a brass screw perpendicular through the disc that tightens up on the back of the stepper motor to lock the X axis it in place.
We use one of these on our Shapeoko 2 gshield to switch between two different stepper motors. Z axis stepper & the encoder stepper for laser modulation.
You would have to use two different grbl axis step/mm settings for the two different axis stepper ratios and the circumference of the Pen’s surface. This is easy to switch back and forth with our PicSender gcode streamer.
Here is an inexpensive 4th axis rotary for a Sherline and it looks like it has a 2 phase nema 23 stepper.
You could make a jig that adapts to the rotary that will hold the pen for rotating it to engrave.
No expensive or complicated software would be needed, because the rotary axis gcodes would not require any A, B or C angular move commands. Only linear X axis step over moves to index the rotary for the next raster line to engrave. Our PicLaser or PicEngrave Pro 5 can generate the X, Y & Z gcode commands needed to engrave from a Black & White image. This would give you the ability to engrave anything (text and a logo) 360 degrees around the Pen’s surface.
Just a thought.