For some reason the 1830 typesetter altered Gidanah, the spelling in 𝓟, to Giddonah. The later misspelling Giddonan in the 1892 RLDS edition is, of course, a simple typo and can be ignored. The name Giddonah actually occurs elsewhere in the text, in Alma 30:23: “now the high priest’s name was Giddonah”. The name also appears as part of the compound name Gid +giddonah, in Mormon 6:13: “the ten thousand of Gidgiddonah had fallen”. (Gid alone also exists as a personal name, in Alma 57–58. It is also possible that Gidgiddonah derives from Giddonah by reduplication of the initial Gid.)
It is highly unlikely that Oliver Cowdery remembered the other Giddonah spelling and told the 1830 typesetter to change the spelling of Gidanah in Alma 10:2 to agree with the later spelling, especially since Giddonah occurs only in Alma 30:23 and, secondarily, in the name Gidgiddonah in Mormon 6:13—and both at some distance from Alma 10:2. And the 1830 typesetter could never have made the change on his own since at any given time he had access to only 24 (or so) pages of manuscript; moreover, he never set type from 𝓞 until he reached those portions covering Helaman 13 through Mormon (that part of the text where the 1830 edition was set from 𝓞). And even if he had had access to the entire original manuscript, it is absurd to think that he would have taken the time to find Giddonah that far ahead in the manuscript and then to decide on his own that Gidanah in Alma 10:2 should be replaced by Giddonah.
A more reasonable possibility is that the 1830 typesetter accidentally misspelled Gidanah as Giddonah (by doubling the d and misinterpreting the an as on). Under this possibility, there would be no reason to reject the reading of the printer’s manuscript here. In particular, there is nothing inherently wrong with the name Gidanah. A similar word ending in -anah is the Book of Mormon word rabbanah, used twice in Alma 18:13 and explained there as meaning “powerful or great king”. The critical text will follow the earliest textual source (here the printer’s manuscript) and restore the spelling Gidanah in Alma 10:2.
Summary: Restore in Alma 10:2 the spelling Gidanah from the printer’s manuscript; the name Giddonah found in Alma 30:23 is simply a different name.