Why Cogitant? 

In 2008 there were already around 1.2 million limited companies registered in the UK and the dot-com era promise of internet riches had led to the registration of more than 7 million .uk domain names.  Finding an name that was available for use both as a company name and a domain name, that was reasonably short and memorable, and that was related in some way to the activity of the new company proved to be quite a challenge.  I came across cogitant during a trawl of Latin words with somewhat relevant meanings - it's the present participle of cogitare, to think - and appears in the OED as a rare English word of the same meaning i.e. "thinking", and also "that thinks".

How do you pronounce it?

For what it's worth, I say it like cogitate rather than like cog. For the linguists among you that's kɒʤɪʈəŋʈ.  Latin scholars differ in their opinions about how the Romans might have pronounced it, so as long as you spell it correctly, pronounce it how you like laughing.