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