Per OP's suggestion I am expanding my comment to an answer. (Of course, it will be nice if someone is able to find some additional information and sources.)
The following is mentioned in Wikipedia article on The Cheesecake Factory:
A fictional version of The Cheesecake Factory is used as a setting in the U.S. sitcom The Big Bang Theory. The show's portrayal of the restaurant, however, is not visually accurate to the real Cheesecake Factory. According to the company, it "does not have any sort of arrangements with the show. The Cheesecake Factory is really pleased to be featured in such a funny and wildly popular show".
Here is a link to the current revision of the Wikipedia article - in the case this information is changed by editing of the article.
Wikipedia gives as a source TV Q&A: ABC News, 'Storage Wars' and 'The Big Bang Theory.' I quote from there:
Q: On “The Big Bang Theory,” Penny works for the Cheesecake Factory, but clearly their version of the Cheesecake Factory is nothing like what it is in real [life] (at least here in Pittsburgh.) At best, I would liken Penny's place of employment to a Denny's. So, my question is, does the show have to pay to use the Cheesecake Factory name? Or better yet, why hasn't the Cheesecake Factory sued the producers for defamation?
- Linda, 39, Castle Shannon
Rob: I've had a similar thought and last night I was at dinner with a friend who brought up how much it bugs her that the Cheesecake Factory on "Big Bang" looks like a Denny's without any prompting from me. There’s no mention of “promotional consideration” paid by Cheesecake Factory in the “Big Bang Theory” end credits so Cheesecake is not paying Warner Bros., which produces “BBT.” And why would Warner Bros. pay Cheesecake when “BBT” gives the chain a ton of free publicity every time it mentions the restaurant by name? True, the Cheesecake Factory restaurant set on “BBT” is smaller and not as spacious as the restaurant but if you adhere to the motto “any publicity is good publicity,” then this is great exposure even if it’s not 100 percent authentic in its presentation.
A spokeswoman for the restaurant chain says, “The Cheesecake Factory does not have any sort of arrangements with the show. The Cheesecake Factory is really pleased to be featured in such a funny & wildly popular show.”