John, my approach varies depending on where the transcription error exists and the type of document.
I guess we are primarily discussing surnames, as forenames regularly vary from document to document especially in Census returns.
If the error is due to an online mistranscription of an original document, especially if fairly obvious, then I will report the error to Ancestry, FindMyPast, FreeBMD, or whatever. Usually, it eventually gets corrected so nothing needs to be adjusted in my data.
If the error is in a Census, probably due to the enumerator getting the name wrong, then I would make a Note in the Source record, but not use the Alternate Name field unless that name became a recurring theme.
If the error is in a GRO Index then I would treat it in much the same way as the Census case above.
I’m not sure if there is any way to correct such mistakes.
If the name is in a BMD Certificate or other formal document then I would probably use the Alternate Name field.