The company name was actually born out of the product name. We were known as 'ibforums' from the outset, so we really had to stick with the initials 'ib'. Invision board was one of the suggestions and it was kinda catchy. Whether that word was influenced by 'envision' I don't know, but I don't think so at the time.
Invision is used by other businesses so we wanted something more unique and that's where the Power came from, so then to reflect the company name, Invision Board was changed to Invision Power Board