I agree with the whole nickname thing. Maybe [name]Jonathan[/name] and [name]Jackson[/name] if you’re really in love with the names.
[name]Jonathan[/name] and [name]Jackson[/name] is brilliant! [name]Jack[/name] is a common nickname for [name]John[/name], as many others have said. I would find it more than a little strange to meet brothers named [name]John[/name] and [name]Jack[/name].
I think to achieve true cheese you would have to do [name]Jean[/name]-[name]Jacques[/name] and [name]Jacques[/name]-[name]Jean[/name]. If you are still worried then maybe try naming one of them [name]Joe[/name]. I know of at least two sibsets named [name]Joe[/name] and [name]John[/name].