I've made a pen myself at a local makerspace. If you have the chance, you should definitely try to do it yourself- it's pretty safe and if once you get the hang of it it's very relaxing.
I have not done it myself, but there are a number of kits out there. Look up "pen blanks". You'll usually need a lathe (often a small desktop one is sufficient for this purpose) and a kit to get started. Once you have a better idea of what you're doing, you will still need the hardware kits (for the nib and ink bladder, or pencil mechanism, etc.) but can branch out into using your own blanks and coming up with your own designs.
