Zarahemla is the correct spelling for this name; there are 40 fully extant spellings of the name in the original manuscript, and each one reads without variation as Zarahemla. In addition, the name is consistently spelled Zarahemla in the printer’s manuscript (151 times), being initially miswritten only once as Zarrahemla by scribe 2 of 𝓟 (in 4 Nephi 1:8) but then immediately corrected by him to Zarahemla. (Two of the 151 instances of Zarahemla in 𝓟 were the result of momentary errors in copying and were crossed out; the actual text itself has 149 occurrences of the name Zarahemla.)
The only misspellings of this name are found in the printed editions. And only one particular misspelling of Zarahemla has ever persisted to any degree: namely, the phonetically identical misspelling Zerahemla here in Mosiah 1:18. This spelling with e rather than a for the first vowel was accidentally set in the 1837 edition and copied into the 1840 Cincinnati/Nauvoo edition as well as into the 1841 British edition, both of which were set from copies of the 1837 edition. Later, in the next chapter of Mosiah, the same misspelling occurred once more in the 1837 edition, but in this second case the error was copied only into the 1841 British edition:
Other misspellings of Zarahemla in the editions are simple typos that have occurred randomly and never persisted:
Summary: All the manuscript evidence supports Zarahemla as the correct spelling for this name.