I will presume you are not Mormon, or other religion that condones polygamy. So when a person says ‘my wife’, we know exactly whom he is talking about.
[color=red]My wife July is here. : “July” is not essential to identifying whom you are talking about, so we surround “July” with commas:
[color=indigo]My wife, July, is here.
[color=red]This is my wife, July : when the nonessential identifier comes at the end of the sentence, as with this sentence, place a comma as you have done.
[color=indigo]My friend Paul is a doctor. : “my friend” is not a precise identifier, and so we need “Paul” to serve that purpose. So - no comma.
[color=indigo]Paul, a friend of mine, is a doctor. : “Paul” is a precise identifier, and so we put commas around the ‘nonessential’ “a friend of mine”.
[color=red]I believe that #1 = I have one friend.
I believe that #2 = I have two or more friends.
The reason why the issue of a comma arises is because, when someone begins, “My friend…”, we don’t even consider the possibility that the speaker might have only one friend in the world.
If we did…then the contention in (1) presupposes that, if the friend is then named (Mona), it is the punctuation (the comma) that conveys meta-information*** regarding the speaker’s lack of social relationships: the use of a comma shouts that I am virtually friendless in the world!
What then, does “I, Bazza, do hereby swear that…” shout to the world?!
I also disagree.
***meta-information: information conveyed that is over and above the obvious meaning of the words.