As Lorna says, the original cannot be changed (if you were indeed contemplating that). Different online sites treat "corrections" differently.
FamilySearch has only just started accepting "corrections" and even then, not for all datasets - it seems to depend on where the index has come from.
FindMyPast only allow one value at once for the index, and that must match the paper original. They will correct a transcript error - if they believe that the new value matches the original. Correcting an error in the original is not accepted by them, nor are other "useful" variants.
Ancestry, on the other hand, allows multiple values for a name on the index, so it is possible to correct errors in the original, or add variations, so that both the original and any corrections point to the same record. So, I can "correct" the Army clerk's rendering of my relative's name - the clerk wrote Pigstock, the index includes that Pigstock, but it now also includes an additional index of Pickstock pointing to that record.
When it came to entering the Source Record for him in Family Historian, I created the title using the name as it is on the paper but added the correct version using "sic" - thus, something like "Muster Roll for Isaac Pigstock [sic - Pickstock] .... " - square brackets being a recognized convention for "this is not in the original".
Whether to add an Alternate Name is a matter of debate. I tend not to do it with one off errors in originals, but consistent variants (such as Pigstock for Pickstock) are another matter.
NB - I've been talking about "errors" in originals (or indexes) but it's often a moot point whether it's an error or a variant.