Do you mean the logo? Because the Starbucks logo was based on the charicter "Starbucks" from the book Mobie Dick. They recently changed the logo though.
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Starbucks has nearly 100 registered trademarks, but the most familiar is their mermaid logo.
Starbucks
starbucks
Starbucks use the mermaid as their logo - although Starbucks actually officially call it by it's proper name - a Siren, not a mermaid.
There is a long, involved history of how the logo was developed. Be sure to read the story of how the Starbucks siren became less naughty, here: http://www.deadprogrammer.com/starbucks-logo-mermaid The wikipedia article will tell you briefly about how the mermaid lost her tail and her navel and chest were "cleaned up" because of an embarrassed elementary school principal. http://en.wikipedia.org/wiki/Starbucks
It is a siren.
The logo that features an "e" and an "a" is the logo of the global coffeehouse chain, Starbucks. The design includes the word "Starbucks" in a unique font, but the "e" and "a" are prominent within the brand's name. Another notable example is the EA (Electronic Arts) logo, which prominently features both letters.
starbucks coffee franchise
There is a long, involved history of how the logo was developed. Be sure to read the story of how the Starbucks siren became less naughty, here: http://www.deadprogrammer.com/starbucks-logo-mermaid The wikipedia article will tell you briefly about how the mermaid lost her tail and her navel and chest were "cleaned up" because of an embarrassed elementary school principal. http://en.wikipedia.org/wiki/Starbucks
The logo on the coffee cup that Gibbs likes to drink does look very similar to the Starbucks logo although I don't think they ever truly say where he gets his coffee from. It is very common for companies such as Starbucks, Pepsi, Nike, etc. to advertise in tv shows and movies.