Tipping is customary in service professions.
You tip your wait staff, your hairstylist, the people who do your pedicures and manicures, the person who prepares your coffee, so why not your tattoo artist?
Most tattoo artists who work in a shop take home only about 50-60% of what they charge you. The rest goes to the shop and the shop owner. Most tattoo artists charge for tattoo time only, and a lot of us spend hours more on each tattoo than the time we get paid for. Since you are not buying an already made product, a lot happens behind the curtains that you probably don't stop to consider. Beyond that, this human being, your tattoo artist, puts their precious and unique creative energy into making your tattoo happen.
Unless of course they don’t. If they are rude, or don’t listen to you, or seem to rather be anywhere else but the tattoo shop tattooing you, by all means, don’t tip them. But if they spent time rearranging their schedule for you, drawing and making changes to the drawing, and changing placement and size, so you could see all of your options. If they discussed the logistics and the details, before, during and after, offered you water or tea, made sure that you were comfortable and warm, that the music was to your liking, that you have all that you need before you walk in and then out of the door at the end of your appointment. If the person tattooing you made all of this effort, feel free to show some extra appreciation. 15-20% of the total tattoo cost is the general rule of thumb.
If you cannot afford to tip (totally understandable), show your appreciation in some other way — send them a thank-you card, drop by with some flowers, share some of your garden harvest, bake something, or make something for them by hand. We all love to display our client's thank yous. We are honored that we could make you happy.