TiVo - the Word
The word "TiVo" has come to be used as a verb in the English language, used as shorthand for recording a program to a DVR, as in "Yes, I TiVo old Seinfeld reruns." But TiVo - the company - has argued against this usage.
Over the years, TiVo has joined the ranks of brands such as Xerox and Kleenex in having the product they produce be so closely identified with the company that produces it, that the company name becomes a substitute for the product.
Technically, TiVo would like people to refer to a hard drive-based recording system as a DVR or digital video recorder, and to only use the word 'TiVo' for their DVRs. To pursue the point, they generally refer to their products as TiVo DVRs.
Originally, the technology that became TiVo was called Teleworld. As the product neared the completion stages, the company decided to adopt the made-up word TiVo. The T and V are said to be from "television," and the i and o from "in" and "out."
The company is specifically called TiVo Inc.