From Middle English Temese, from Old English Temes, Temese (compare Welsh Tafwys), from Latin Tamesis, Tamesas. Variant spellings with h arose in Middle English due to the mistaken assumption of a Greek etymology.
The Latin name is possibly from Proto-Celtic *tamesās ("river, waters"), a masculine ā-stem of *tames, Proto-Indo-European, zero-grade of *témHes-, *témHos, an s-stem from the root *temH-. Related to Proto-Celtic *temeslos ("darkness"), *temos. A parallel in Proto-Celtic of "dark, darkness" taking on the figurative meaning of "water" can also be found in Proto-Celtic *dubros ("water, dark"), from Proto-Indo-European *dʰubrós ("dark"), yielding Welsh dŵr ("water"), Irish dobhar ("water, sea, dark, gloomy").
Alternatively from Proto-Celtic *tā-, *tāyo-, from Proto-Indo-European *teh₂- ("to melt"), or from unknown non-Indo-European root.
Possible cognates include the names of rivers and tributaries such as:
Taff, Tamar (from Latin Tamarus), Tame, Tavy, Team, Teifi (from Welsh Teifi, from Old Welsh Tebi, Teibi), Teme, and Teviot (Latin Tefius, Teifius) in Great Britain
Tambre (from Latin Tamaris), Támega (in Galician, Portuguese Tâmega, Latin Tamice), Támoga or Támboga (Latin Tamega), and Tamuxe, all of them flowing through Galicia (Spain) and northern Portugal