This is a special name given by Oxonians (especially the ones you see rowing about all the time) to a river everyone else calls the Thames. The name applies only within the limits of Oxford itself; although a few people attempt to apply the name to the river above a certain point (sometimes, Dorchester, other times its junction with the Cherwell), people outside the immediate affect of Oxford call the river Thames all the way to its source in the Cotswolds.

No-one really knows where the name came from. Was it the real pre-Roman name of that part of the river? Did the residents of Oxford decide, for reasons lost to history, to abbreviate the Roman name for the river (Tamesis) differently? Did a don (who clearly had too much time one his hands) attempt to render 'Ouse' in a Classical language?

En subito frontem placidis e fluctibus Isis
Effert, et totis radios spargentia campis
Aurea stillanti resplendent lumina vultu.
Iungit et optatae nunc oscula plurima Tamae,
Mutuaque explicitis innectunt colla lacertis,
Oscula mille sonant, connexu brachia pallent,
Labra ligant animos. Tandem descenditur una
In thalamum, quo iuncta Fide Concordia sancta
Splendida conceptis sancit connubia verbis.

16th-century English poet William Camden's poem Connubium Tamae et Isis describes the "marriage" between 'Isis' and 'Tamae' (the river Thame, a tributary of the Thames). Isis flows down from his source, a rather elaborately decorated cave in the Cotswolds. Tamae flows down from her source on the northern slopes of the Chilterns, by the town that bears her name, and they are 'married' where the rivers meet in Dorchester. As the river flows by London at the end of the poem, there is no 'Thame' or 'Isis', only Tamesis, bringing to mind the Greek myth of Hermaphroditus. (Geomorphologists with too much time on their hands occasionally speculate as to whether this is recognition of an ancient stream piracy event). Camden's poetical allegory may be the origin of the name, or he may have borrowed it from local usage. Whatever the case, the name Isis now has Spenserian Authority after its appearance in The Faerie Queene.

1911 encyclopedia - River Thames

Dana F. Sutton, University of California, Irvine
William Camden, Poems and Epitaphs: A hypertext edition