In genealogy the practice is to always use standardized (i.e. modern) versions of names. Standardized in the language that the names bearer spoke. In this case Johann Peter is what you enter in your genealogy program. The same applies also for those who emigrated to other countries. German born persons with names like, for instance, Karl, Heinrich, Wilhelm or Jürgen should be written so, even if they left Germany for the Americas, and not as Charles, Henry, William or George. The names of their children born in the new countries are of course written with English name forms though.
There is one exception, though: kings and queens, emperors and other royalty. If you have Friedrich der Große in your genealogical material, you may write his name as Frederick the Great, if English is your language.