And it isn't palindrome. It might be a sub-category of anagrams. Couldn't find a definitive answer online. What do you call a word that spells another word when read backward? For example: stressed <-> desserts.
Here's something I found online, but I'm not sure how authoritative it is: http://users.tinyonline.co.uk/gswithenbank/backword.htm
Personally, I like emordnilap … has a nice self-referential twist to it.
Interestingly, the header on the page you've linked to lists Janus words as one name for these reversible words, but the common definition of a Janus word is one that has opposite or contradictory meanings. Cleave is commonly cited as an example, as is sanction. I'm just killing time here, hoping that the answer to your question will come to me, as I'm fairly sure I've encountered a name for such words. Doesn't seem to be happening. Yes, emordnilap has a certain charm.
Semordnilap (pl. semordnilaps) appears to be the more popular take on your idea, and dates at least to 1961.
Other names for such words are: volvograms, heteropalindromes, semi-palindromes, half-palindromes, reversgrams, mynoretehs, reversible anagrams, word reversals, or anadromes. Most of these sound wrong to me, either to my reason, or to my taste. I will go with semordnilap.
But my research led me to ambigrams, a completely different animal, more visual than literal. The better examples of these have quite a bit of charm! Perhaps not enough charm to make me want a tattoo, but who knows? I must say that an ambigram does make a lot of sense for a tattoo. Tattoo ambigrams
Glenn: I do believe semordnilap is the word, after following up on your links, and also finding this one.
BTW, a friend of mine who teaches classical languages cracked up when I maintained the plural of emordnilap is semordnilap, and not emordnilaps. But then, who's following any standard rules on this abstruse concept?
On the topic of ambigrams, which are fascinating but sometimes (for me) hard to visually "synch," yeah … as a tattoo it would make perfect sense. Either as a reflection ambigram (when looking at yourself in a mirror) or as a rotational ambigram (depending on body position).
If you want to see some great examples of ambigrams, check out Hofstadter's book Metamagical Themas.