Geographical features do not really have "official" names, there has never been any formal control over granting and controlling them. These names usually began a long time ago as a description or definition of the feature and have been modified over the years.
I suggest you quote the source you regard as authoritive. eg Ordnance Survey, Local Authority, River Board (though these may not always be consistent). If this is a quiz, it would only be fair to accept either version.
The river from Hertfordshire through East London to the Thames has a similar problem with its name. As a river it is often referred to as the "Lea", as a navigatable waterway, the "Lee", but not entirely consistently. If officialdom cannot sort out the name of this well known, well used river, there's probably no chance of deciding on Arle / Alre!