die Tätowierung
tattoo
A design, image, or lettering that is permanently applied into the skin with ink or other coloring agents.
Sie hat eine kleine Tätowierung eines Ankers am Handgelenk.
She has a small tattoo of an anchor on her wrist.

tattoo
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tattoo
A design, image, or lettering that is permanently applied into the skin with ink or other coloring agents.
Sie hat eine kleine Tätowierung eines Ankers am Handgelenk.
She has a small tattoo of an anchor on her wrist.

'Die Tätowierung' (the tattoo) belongs to the word family around the verb 'tätowieren' (to tattoo). A person who does this as a profession is 'der Tätowierer' (the male tattoo artist) or 'die Tätowiererin' (the female tattoo artist).
Er ließ sich von einem berühmten Tätowierer ein Kunstwerk stechen.
He had a work of art tattooed by a famous tattoo artist.
You distinguish the two meanings by context. If people are talking about the design, the size, or the place on the body, they mean the image. If it is about the duration, the pain, or the cost, they mean the process of tattooing.
Ihre neue Tätowierung zeigt einen bunten Schmetterling.
Her new tattoo shows a colorful butterfly.
When 'die Tätowierung' (the tattoo) is meant as an image on the skin, it is often combined with the verbs 'haben' (to have), 'tragen' (to wear), 'zeigen' (to show), or 'entfernen lassen' (to have removed).
Er hat eine große Tätowierung auf dem Rücken.
He has a large tattoo on his back.
To describe the process, the construction 'sich eine Tätowierung stechen lassen' (to get a tattoo) is often used. Here, 'sich' is in the dative.
Nächste Woche lasse ich mir eine neue Tätowierung stechen.
Next week I'm getting a new tattoo.
tattoo
'das Tattoo' and 'die Tätowierung' often mean the same thing: a permanent picture, symbol, or word on the skin. 'Tattoo' sounds very normal and modern in everyday speech. 'Tätowierung' sounds a bit more formal or factual and can also refer to the process of getting the tattoo done. When you are talking about the image on the skin, you can usually use both words. In conversations among friends, 'Tattoo' is often more natural.

Nach der Tätowierung sollst du die Haut gut pflegen.
After the tattooing, you should take good care of your skin.
Lisa zeigt mir ihr neues Tattoo am Arm.
Lisa shows me her new tattoo on her arm.