Whence the name?

So let's take it one word at a time:
Polymetis ... Thoughtware ...

Polymetis

The name Polymetis is derived from classical Greek; definitions are from Liddell and Scott's Greek-English Lexicon (OUP 1905)

πολυ- (poly-) means, as most people know, many.

μητις (metis, where the e is long, Greek letter η eta) is a noun meaning

1. counsel, wisdom, skill, cunning, craft
2. a plan, enterprise

Hence πολυμητις (polymetis), which is an adjective, means (as the Lexicon has it) of many counsels or expedients, ever-ready. This word

1. was used (in Greek) repeatedy to describe the hero Odysseus in Homer’s Odyssey with the meaning resourceful;
2. was used (in English) in the title of a work published in 1747 by Joseph Spence entitled Polymetis: Or, An Enquiry Concerning the Agreement Between the Works of the Roman Poets, And the Remains of the Antient Artists. Being an Attempt to Illustrate them Mutually from One Another.In ten books.

Thoughtware

Thoughtware means what it says: thoughts are my wares or I think for a living. Our work is always of the kind that needs a lot of both knowledge and careful thought. A web search of the word using AltaVista came up with 42 references; several are companies in the USA with names that include the word, so clearly nobody has any legal claim to a monopoly of it. However, as far as we know, Polymetis Thoughtware Limited used the word first.

Note that Polymetis Thoughtware Limited had no legal or business connection with any other company using either the word Polymetis or the word Thoughtware in its name, or with any product or service offered by any other company under any name containing either of these words.