Origin of Names

Twitter: The original project code name for the service was twttr, inspired by Flickr and the five-character length of American SMS short code. "[W]e came across the word 'twitter', and it was just perfect. The definition was 'a short burst of inconsequential information,' and 'chirps from birds'. And that's exactly what the product was." - Jack Dors;'ey.
Google: In 1996, Larry Page and Sergey Brin called their initial search engine "BackRub," named for its analysis of the web's "back links."Sean and Larry were in their office, using the whiteboard, trying to think up a good name - something that related to the indexing of an immense amount of data. Sean verbally suggested the word "googolplex," and Larry responded verbally with the shortened form, "googol" (both words refer to specific large numbers). Sean was seated at his computer terminal, so he executed a search of the Internet domain name registry database to see if the newly suggested name was still available for registration and use. Sean is not an infallible speller, and he made the mistake of searching for the name spelled as "google.com," which he found to be available.
Facebook: The name was inspired from the custom of universities in USA to give their newly enrolled students a paper Facebook introducing people on the Campus to them.
Yahoo!:  The name Yahoo! is an acronym for "Yet Another Hierarchical Officious Oracle," but Filo and Yang insist they selected the name because they liked the general definition of a yahoo: "rude, unsophisticated, uncouth." Yahoo! itself first resided on Yang's student workstation, "Akebono," while the software was lodged on Filo's computer, "Konishiki" - both named after legendary sumo wrestlers. 
Yelp: The project arose out of research into the local services market by David Galbraith, who worked with Jeremy Stoppelman on the early stages of the project and chose its name as a contraction of Yellow Pages.
Wikipedia: "Wiki" means quick in Hawaiian. The Wiki Wiki Bus is Honolulu International Airport's shuttle, and has shuttled people between the Main Terminal and the Domestic/International Terminals since the mid-1960s. The "pedia" part is from the word encyclopedia.
Amazon:  founder Jeff Bezos renamed the company Amazon (from the earlier name of Cadabra.com) after the world's most voluminous river, the Amazon. He saw the potential for a larger volume of sales in an online (as opposed to a bricks and mortar) bookstore.

I don't think there is a science to naming businesses, maybe sometimes but not always.