To play devil's advocate, such a thing as transcribing Western names phonetically using Chinese characters does exist, both in contemporary Chinese and in other historical or minority Chinese-derived languages, as well as in old Japanese.

Here are the current rules for standard Chinese:

https://en.wikipedia.org/wiki/Transcription_into_Chinese_cha...

And here is some information about the same thing historically done in Japanese:

https://en.wikipedia.org/wiki/Ateji

That being said, I have only glanced at that tattoo table and it seems wildly inaccurate and simplified. But the underlying concept does exist.