According to the International Business Times, before Tesla took control, the Tesla.com URL was owned by Stu Grossman, perhaps since 1992. The popularity of the Tesla name caused him some legal hassle in 2005, when Tesla Industries, Inc., a "manufacturer of portable electronic ground power units," tried to get the domain. The company submitted a complaint to the National Arbitration Forum and said it should be allowed to use the name because, among other things, it was, "known by the name "Tesla" by all branches of the U.S. military, certain foreign military, the U.S. Forestry Department, a number of police departments, and the U.S. Department of Homeland Security." Grossman responded that that the word "Tesla," is "the standard SI unit of magnetic flux density, thus a generic term," and that a lot of companies use it. Grossman was able to keep the name and, well, we all know a different Tesla today.
This isn't the first time Tesla has had to deal with someone else bogarting the Tesla name (somewhat ironic, that). When the automaker started doing business in China, it had to use the name Tuosule for a short while because "Tesla" was registered there by a trademark troll in 2006. A deal of some sort was later reached and Tesla is proudly Tesla in China now. As for what might have transpired between Tesla and Grossman over the Tesla.com URL, no one is talking.
UPDATE: Tesla CEO Elon Musk has thanked Grossman via Twitter:
Just wanted to thank Stu G for https://t.co/7FlnbruWpL. Know it meant a lot to you. Will take good care.— Elon Musk (@elonmusk) February 21, 2016