In Islam it's haraam/not permitted coz it's altering God's creation and a form of deception. It's also considered haraam coz it causes unnecessary pain and possible infection......hey that rhymes! Henna and other temporary tats are ok as long as they don't contain inappropriate images.
Mutilation for the sake of beautification is haraam. What about earrings? Well they are permitted for women coz earrings aren't permanent (also dyeing hair). Braces to change/fix one's teeth is ok too for the medical benefit.
If a person was to turn to Islam, however, and is covered in tattoos it's not necessary to have them removed coz prior sins will be forgiven. Tattoos don't affect wudu (ablution) since it's under the skin.
Lastly, we really don't need to write God's name on our bodies when it's already written on our hands
SubhanAllah!