The Word "Droid" is a Registered Trademark of LucasFilm Ltd.
Shortly before Verizon launched their DROID line of mobile devices, Lucasfilm Ltd. filed a trademark on October 9, 2009, for the term “Droid." Specifically, they claimed the term for:
Wireless communications devices, including, mobile phones, cell phones, hand held devices and personal digital assistants, accessories and parts therefor, and related computer software and wireless telecommunications programs; mobile digital electronic devices for the sending and receiving of telephone calls, electronic mail, and other digital data, for use as a digital format audio player, and for use as a handheld computer, electronic organizer, electronic notepad, and digital camera; downloadable ring tones and screen savers; cameras, pagers and calling cards.
As a result, Verizon paid Lucasfilm Ltd. (and now Disney) an undisclosed sum for the rights to use this word as a brand name.
The word “droid” is an aphesis form of “android,” a word that’s been around since at least the 1700s. The first documented mention of “android” is in the Ephraim Chambers’ Cyclopedia, “Albertus Magnus is recorded as having made a famous androides.” Android derives from the Greek ????? (andro-), meaning “man,” and the suffix -????? (-eides), meaning “form, likeness, appearance, or resemblance”—hence the definition of android being “automaton resembling a human being."
The word “droid” was first used in Star Wars: A New Hope, which came out in 1977. That's why Lucas was able to trademark the word, even though it wasn't used to describe a wireless communication device (unless the particular droid was being used to relay messages wirelessly; I suppose the Imperial Probe Droid in Empire Strikes Back might have had that capability). You’ll note that unlike in most other science fiction where an android signified a machine that resembled a human, Star Wars’ droids did not need to resemble a human (though some did).