While a tattoo can be made with a pen, it is not recommended. Not all pen inks are safe or durable for such use. A pen would also be difficult to sterilize properly.
Properly done, tattoos are generally safe. Nonetheless, tattoos carry certain health risks. Even inks and dyes that are considered safe can cause allergic reactions, bumps (called granulomas) and keloids (scar-like areas of raised skin). Because the needles or other piercing instruments can transmit bacteria and viruses past the barrier of the outer skin if not properly sterilized, a tattoo can lead to a skin infection or transmission of a bloodborne infection such as hepatitis C or tetanus. For these reasons, medical professionals generally advise that tattoos be done only by licensed professionals.