In Welsh the Gamber is apparently known as the Amr (Note). There is actually a second stream of the same name: the Amir or Humir near Newport. The following references from the Liber Llan Dâv* (See Other Works) indicate the name...
Cemeis [Inferior]. Its boundary is: Aber Humir on the Usk along to its source. Along the Usk as far as Aber Nant Bichan [Vychan*] as it leads upwards to the breast of the Allt towards the right to the Ard through the Dou Ciuiu [Civiw*]. Along the Arhit [Ard*] throughout its length to the breast of the Allt, making for the source of Nant Humir, that is Nant Merthir, where the boundary began.
Merthir Ivn [Julii*] & Aaron. Its boundary is: The head of the dyke on the Usk, along the dyke to the breast of the hill, along the the dyke to the source of Nant Merthir, that is Amir. From its source to the pant, upwards as far as the source of Nant Lechou [Llechè*]. Along the Lechou downwards as far as the mouth of the pant on the right side. Along the pant upwards as far as its head, to the dyke, along it towards the West to the shoulder of the Allt, to the source of Nant Beth yr Alltudion [Alltudjon*], along the Nant to the Usk. Along the Usk with its wears as far as the head of the dyke where began.
The first location is Kemeys Inferior, which, despite the Ordnance Survey shifting the label on modern maps, is on the east side of the River Usk, where Kemeys House is marked. The second location is the parish of St. Julians, some 3km to the south west of Kemeis.
There are a number of interesting questions raised by these references. The first is the location of the Amir. To identify this we would ideally need to identify the Dyke, Nant Bichan, the Lechou, and Nant Beth yr Alltudjon, and decide what was meant by Ard and Allt – the latter of which can mean "hill", "hill-side", "cliff", or even "wood". At the worst we can estimate the location as being a confluence large enough to be well known and named, and as downstream of Kemeys. The Cemeis reference is part of a grant record, which denotes the area given as ~900m2 and between the wood, field and water. This suggests it is the strip of land next to the Usk, below Kemeys Graig. If this is the case, it is likely that the Amir is the stream ending near Aber Nant Farm (Map) which sources above Cat's Ash on a Roman road that has had near continuous use since the occupation, or that it is the stream that ends at [Great] Bulmore [Farm]. Interestingly the latter is marked on the 1st Edition OS map as "Tomb, site of", but we can't get too excited about that as the stream wouldn't have been within Ercing.
The second thing to note is the Humir / Amir name. "H"s before vowels were relatively disposible in the Glamorgan area and surroundings*, and here we see evidence of this. This dropping might suggest the Gamber / Amr has an etymology inline with rivers like the Humber. While it is not entirely clear where the name Humber comes from, there are a sufficiently large number of Humbers in Britain to suggest it is a pre-Saxon, if not pre-Celtic term, and comparison with other common river names like Avon suggests it might mean something like "river". There is, interestingly, a Humber Brook some 20km north of Hereford (passing, for example, through the village of Humber) – though there is no evidence of a tomb at its head.