I'd really like to see how exactly it's backwards, but if it is He-Wav-He-Yod, it could mean a number of things instead of the tattooist just getting YHWH wrong. I mean, who the fuck would have the tetragrammaton tattooed on them, anyway?
It could mean 'my desire', which would make sense in her context. It could also mean 'my destruction'. It could possibly be a suffixed perfect of 'I am (me)', whereas Yahweh comes from the imperfect tense (I will be--). Maybe. I really want to see it.