If there is a name ('Bob', say) and it is used in the year 300, and then 1200 years later in the year 1500, the name 'Bob' is recorded, it does not follow that they are the same name. They are just the same spelling.
In this case, 'Alun' (early) is a river name from a personal name. 'Alun' (late) is an adaptation of the name Alan, from the Breton 'Alan', influenced (possibly) by the river name Alun, but not deriving from it (sorry).
Dyfyr ap Alun Dyfed is from the 'Dream of Rhonabwy'. Which is a medieval text believed to have been written no earlier than the 12th century. E.g. after the arrival of all the Norman Alans. It's also a satire - most of the names aren't 'real', they are intentionally 'aged', and a tad 'mythical'. There are probably other river and place names in there - I haven't looked at the text recently.
I fail to see the point behind your introduction of the fact that the Welsh were living all over the British Isles until the Anglo-Saxon invasion (600-800ish), when the name 'Alun' is not recorded anywhere (England, Scotland or Wales) except in the river name from the earliest records (including inscriptions, from about 300AD on) and 'Alan' is not recorded until after the arrival of the Normans in 1066. Perhaps you'd like to explain how this is relevant?