As above, you have a Pecke-11 and a Peck-849.
You have documents under both variants (cool, thank you), possibly have documents he executed (wills, deeds, etc.) in some way under both variants. The inventory of his estate may report whether he owned books.
We don't all approach this the same way. I would consider those documents, etc. If he seemed to use both variants, then I'd consider the value of the ID with the lower number. How you decided upon the variant can be added to the narrative.
As you indicated in the post, regardless of the iD agreed upon, you plan to report the alternative variant as an other last names.