Upstream of Broad Chalke is a place called Ebbesbourne Wake. I haven't been there yet. It is listed in the Domesday Book as Eblesborne, and its name is clearly connected to the river Ebble. A local historian has suggested that, since 'bourne' means stream, therefore 'Ebble' refers to the name of the person whose land the stream flowed through, during the Anglo-Saxon period. I don't believe this at all.
From the little I know about place names in England, it seems that a lot of rivers have kept the name they had from well before the Anglo-Saxon period, and before our language changed to English.
A great example is the number of rivers in England called the Avon. (One of these runs through Salisbury, and the Wylie, Nadder and Ebble all join it.) Avon corresponds to the current Welsh word Afon, which means river. So it seems people living near the various river Avons (who would have once spoken a language that resembled Welsh more closely) were simply referring to their rivers as ‘the river’.
Similarly, there are the rivers Tame, Thame, Team, Teme, Thames and Tamar. These names are so similar that they probably share a plain, descriptive meaning.
Another reason I'm suspicious: Ebble is onomatopoeic, like trickle, pebble, tumble, babble, ripple. The feel of the word in my mouth, and its sound, is like a shallow stream flowing over a chalky bed. And Ebble is similar to the word ‘ebb’ as in ‘flow’. They may not have evolved from the same common word, but they could both be human attempts to describe a watery movement.
Further thoughts
1. After writing all this, I've discovered there is a river in South Wales called the Ebbw (which would be pronounced 'ebbu'). I have no doubt that Ebble was once a word that described the way the river was. (2018-10-03)
2. I've just discovered a place 20km south of the Ebble called Ebblake. The word 'lake' suggests 'ebb' is describing water. (2018-10-07)
3. I've searched the Gazetteer (2018-10-11) for placenames containing 'ebb', and found:
- Ebberley, Devon which sits at the head of a small stream.
- Salterhebble, West Yorkshire, which sits on the Hebble Brook.
- Stebbing, Essex, which sits on the Stebbing Brook. Downstream there is a Stebbingford (Farm and Bridge) which suggests the stream has been known simply as the Stebbing.
- Ebley, Gloucestershire, which sits on the river Frome.