Welsh and Brittonic are two similar languages, but they are not interchangeable.
You seem to be missing the obvious. The medieval Welshman using the Breton name Alan was NOT referring to the early Welsh name Alun BECAUSE HE KNEW NOTHING ABOUT IT. Most medieval people could not read, and certainly did not go in for etymological trips round local river names. The only names they knew were the names of friends and family, and powerful people. The medieval Welshman did not use the name Alun because he did not know of a Welsh name Alun, and he did not know any Welsh men called Alun (if they existed, they would have died at least 500 years before his time). That is the significance of the time gap. Nor would he have named his child after the river, even if he knew of the river. Medieval children were not named after rivers; they were named after family, friends and powerful people. The modern Alun is the medieval Alan, and widely recognised as such. When people are named Alun in medieval texts in modern Welsh editions, you can be sure that the name in the original text is Alan.
There is no etymological connection between the early Welsh Alun and the medieval Breton Alan.
Your son may well be called Alun, and your father, and his father. I'm afraid it doesn't give you any advantage in actually knowing about the name, any more than being called Hiawatha would mean that you knew something about the name Hiawatha. Doing some research is the only thing that will tell you about a name. And that research has to be more than reading modern Welsh babyname books or listening to modern Welsh popular belief about names, most of which is substantially incorrect. Unless your family tradition of Aluns goes back a thousand years (unlikely) it has no bearing on this question.
You named your son Alun after your father, and because you felt it was a Welsh name. It's a Welsh name by usage; but not by origin. ;)