Oglumuzun ismi  Muhammed oldu hayirli ugurlu olsun

My attempt

Our son´s name was Muhammed. Good luck with him, may he bring you joy.

In my opinion olmak must have the meaning of entering into a state here (otherwise there would be idi). So my guess is

                    Our son was given the name Muhammed...

But I am not quite sure, maybe Henry´s sentence can have this meaning also.

This sentence sounds weird. "Our son´s name has become Mohammed, may it be beneficial and fortunate(for him)" It sounds weird in English too. I would say "Oğlumuzun ismini Muhammed koyduk."

Yes, the use of oldu seemed stange to me as well. Maybe he changed his name later, because he didn´t like the name he was given. 

I don´t guess so. But everything is possible My explanation is simple: His Turkish sucks.

That´s why I couldn´t get it!^^ it is  a turkish friend who has been raised in France. But he is used to talk with his turkish family though :s

Maybe he should talk to you in French. Much simpler for you 

the difference between

" adını ... koyduk" we named him as ...

and

"adı ... oldu." he was named as ...

about second sentence: they were discussing names to name their son such as ahmet mehmet ali veli... but they are not sure which one to name. at the end they decided a name after long discussions. that is why they dont simply say we named him as something. as i understand he was named after some discussions. so they used the expression "...oldu"

It is possible but you know my simple explanation . I think "our son´s name" has to be an object instead of being a subject.