Six Mandaic letter names do not follow the alphabet's own naming plan: ushenna, aksa, it, in, dushenna and kad. The other nineteen are formed from the letter's sound with a preceding a, which is a scheme so regular that it looks designed. The six that break it are worth grouping, because they break it in different ways and for different reasons.
Dushenna and kad are the two ligature letters, and their names come from what they were made to write rather than from how they sound. Ushenna and aksa are two of the three vowel letters, and both carry names that a sound-plus-a scheme could not have produced for a vowel anyway. It and in are the two letters standing where the old pharyngeals were, and both are built on the vowel i rather than on a.
That leaves a pattern inside the exceptions, which is more interesting than a list of irregularities. The letters with unusual names are the letters doing unusual jobs: the vowels, the old gutturals, and the ligatures.
None of this tells anyone what the names mean, and for most of them there is nothing to mean. A name that says how to pronounce a letter is not a word with a sense, and the temptation to read significance into these names is one the atlas declines. Where a Mandaic letter name does carry a sense, as dushenna and kad do, the atlas records it.