The river Rother of Derbyshire (Roder, -ir, -yr, -ur 13th cent., Rudde 1330, Rodelle 1330, Rother 1577) is explained by Ekwall (English River-Names 348) as 'chief river', British *dubro- 'water' with intensive *ro- from *pro-. Cameron (Place-Names of Derbyshire 15) agrees with this analysis but suggests 'great river' as a better translation.
I have never been there, but maps suggest that the Rother is not a particularly great river, nor the chief river of Derbyshire. Also, the contraction of the name required is rather violent, since Dubris is still Dover. I wonder whether the meaning of Rother is rather 'red', a rhotic extension of zero-grade *h1rudH- as in Greek and Latin (or with an intervening laryngeal in Sanskrit).
I cannot find such a Celtic formation in Matasovic', but this name need not be Celtic. In disagreeing with Ekwall on the Wye, Jackson considered a Celtic etymology unlikely and pointed out that there were people in Britain before the Celts.
But if the Rother is green, it will embarrass my explanation.
DGK