Personally, I call the little dot over the lower-case "i" "the little dot over the lower-case 'i.'" The Oxford Interactive Encyclopedia defines this mark as follows:

The dot over the lower-case i is derived from a diacritic mark, like an acute accent, used in Latin manuscripts to indicate the i in positions in which it might have been mistaken for part of another letter. The same cause led finally in English to a kind of scribal canon that i must not be used as a final letter, but must in this position be changed to y, though in inflected forms, where the i was not final, it was retained (hence city, cities, duty, dutiful, etc.).

This still doesn't give us a name, but now we understand why it is there, sort of.