You should not blindly accept the authority of something that you find on the internet, and this is a good illustration of that. Each of the web pages listed in this section gives an apparently authoritative derivation of the name of the River Thames. None of them admit in any way that there may be alternative derivations. Yet the derivations are clearly in conflict with each other. There is no particular order to these; they are numbered simply for reference and to show how many that there are. One of these derivations may actually be correct, but there is no way to tell from these web pages if that is so.

1. Celtic for "Tranquil River" or "Smooth River" (Source: Sacklunch.net)
2. Celtic for "Dark River" (Source: KryssTal.com)
3. Meeting of the Rivers Tame and Isis (Source: Last-Names.net)

After seeing the above pages, it is encouraging to see pages that do admit to uncertainty.

1. Similarity of Names of Thames, Tame, Tamar Rivers - "Tame" is Celtic for "Dark One" or "Dark One" (Source: The-River-Thames.co.uk) - This reference (by Ian and Dot Hart, who are avid Thames boaters) is probably the best open-minded consideration of the origin of the name that I found on the web. So here is the text in its entirety:

   "The origin of the name 'Thames' is not fully known. Before the Romans came it was called 'Tems' but the Romans latinised it and called it 'Tamesis'. Various names have appeared since then. The name 'Tamyse' was popular in Anglo-Saxon times but it has been known as 'Thames' since c.1600. When and why the 'h' was introduced is not known. It was once suggested that the Roman word 'Tamesis' derived from the joining of the word 'Isis', an alternative name used by some for the River above / around Oxford, and the 'Thame', the tributary that meets near Dorchester but there is no foundation for this idea. Most etymologists now appear to agree that the name 'Thames' is derived from the Sanskrit (ancient Indian) word 'Tamasa' meaning 'dark river' or 'dark water' and that the use of the word spread from India through the Celts to Britain.

   "Whilst on the matter of the name of the River Thames, it is worth mentioning that the name 'Isis', which some people call the Thames above Oxford, appears to be quite facticious. It has no historical foundation. There is no record of the name in any early charter, it was not used by the Romans or Saxons and does not appear before the 14th century when it first appeared as 'Isa'. It seems it is a name conjured up by scribes in the 14th century for some unknown reason."

2. Magyar origin of the name (Source: The Journal of Hungarian Studies (1997 Issue #1): "The Magyar Origin Of The Western European River Names" ) - It seems very speculative but could be true. "Nedû" is the Magyar word for "liquid", and the authors think that the "reciprocal" (I have no idea what that is) of "nedû" could be the source of the names of not just the Tame, Tamar and Thames in England but also England's Don, the Duna (Danube, Donau) in Hungary, the Don in Russia, the Tana in East Africa, the Szamos in Transylvania (Erdély), and even the Tanais, an old name for the Volga River.

3. Similarity of Names of Thames, Tame, Tamar Rivers - "Tame" is Celtic for "Dark One" or "Dark One" (Source: ManchesterOnline.co.uk)

4. Origin of the name of the town of Thame (Source: ThameHistory.net) - A very interesting consideration that brings in many similar names that do not appear in any other web page that I found on the name of the Thames.