AHA! I cracked it! I have no idea if anyone has ever figured this out before, but:

My name IRL, Tucker, translates to Dilgan. Dilgan in English translates to Temkyh. This translates from English to Al Bhed, as "Dasgor". Dasgor translates to Tyckun (which I thought sounded awesome). Anyway, notice a pattern yet? T-D-T-D, and on. Well, Tyckun translates to Dolgih. Dolgih translates to Tumker! Getting closer... Tumker translates to Disgan. Disgan translates to Teckyh. This translates to Dalgor. Dalgor translates to Tymkun. Which translates to Dosgih. Now, here it is:

Dosgih translates to Tucker!

Al Bhed and English DO have a cycle between eachother! I checked many other words, and the longer the word, the longer the cycle is!

Good to Kuut to Giid to Keet to Gaad to Kyyt to Good!

See how the cycle is shorter?

So, was this discovered in the past? I'm really obsessed with Al Bhed, and actually can speak it IRL.