The names in this atlas for the Mandaic letters are the names the modern character standard uses, and that standard has to write every one of them in plain Latin letters with no diacritics available. Several names in the alphabet are shaped by that constraint rather than by anything in Mandaic.
Att is one. The ninth letter and the twenty-second letter both write a t, one emphatic and one plain, and a scheme without diacritics cannot mark emphasis. So the emphatic one is spelled with a doubled t and the plain one with a single t, and a reader who knows the conventions of Semitic transliteration, where a dot under a letter would ordinarily do this job, has to be told that the doubling is standing in for the dot and does not indicate a long consonant.
Asz, the eighteenth letter, is the same situation. It writes an emphatic s and is spelled with sz to keep it apart from as, the fifteenth. Nothing in Mandaic corresponds to the z.
The Syriac sixteenth letter, recorded simply as E, is the extreme case of the same pressure across the alphabets in this atlas.
None of these spellings is wrong, and all of them are worth flagging, because a reader meeting att and at in a list can reasonably conclude that one is a doubled form of the other. It is not. They are two letters, thirteen places apart.