Two of the twenty-two Samaritan letters are named for a sound that is not the sound their Hebrew counterparts write. The sixth is Baa where Hebrew has vav, and the seventeenth is Fi where Hebrew has pe. Four more, Alaf, Iy, It and In, are named in a form that has lost the throat consonant the letter was made for. Nothing about the writing changed in any of those cases. The letters are the same letters, in the same positions, with the same numeral values; what changed is how the community says them.
That is worth stating plainly because letter names are usually treated as fossils, inherited words that carry no information about the people using them. In this alphabet they carry a good deal. They are the names the Samaritan community teaches, and they were adopted for the letters in the international character standard, so the encoded names of the script are the community reading rather than a Hebraist transliteration. Anyone comparing a Samaritan alphabet chart with a Hebrew one and expecting the names to match will find six that do not, and every one of the six is telling them something true.
The general shape of the phenomenon is ordinary. A script is conservative and a spoken tradition is not, so over enough centuries the two come apart, and the letter names sit in between recording where the seam is. What is unusual here is that the reading tradition is still being spoken, so the seam can be examined rather than inferred.