I don't think that's a problem. Do people think that when they buy books over the internet that they get shipped from the Brazilian rainforests? Do people think the most important thing on Facebook is a portrait gallery?
"Tuna Safari" is a great brand for many reasons - it's cute, it's quirky, it's easy to remember - but those reasons don't include it being descriptive of the product or service. "Tuna" and "safari" are two words that just don't go together - people aren't going to think that you are offering overland trips through Africa to see a saltwater fish. (Anybody who does think that probably isn't someone you want to do business with)
Also, is it worth giving up the Keyword for a good brand?
Absolutely. You might get a tiny tiny benefit from having a descriptive keyword in your branding and domain, but you'll get much more benefit from having a good brand that people connect with and remember and go back to. The content is where you describe your products and your services - in the text, in the headings, in the navigation, in the structure, in the meta description, in the inbound link context. If you try to keyword-stuff the brand and domain name as well, it starts to look uninspiring, robotic and even spammy. Let the brand be creative. Let the brand live.