In a sense, it is extremely important. In another sense, it is of minor significance. Let me solve the puzzle!
A brand name is required for the same purpose a person requires a name: identification. Once a name helps to identify a product, the reputation of the product is gradually built upon its name over time. The name is gradually promoted and surrounded by its superiority, functionality, image and positive perceptions of customers. At the end, the name represents a meaning, an image, a perception that were absent on the day it was born and appeared in the market. It reminds me of the eternal truth in branding: “a brand is what it does”. What a brand does becomes an entangled element in its name.
Take the example of internet giant Yahoo! Now why do you think I have put an exclamation mark (!) at the end of yahoo brand name? The history is quite interesting. Its founders (Jerry Yang and David Filo) were refused patent for the brand name “Yahoo” because this name was then already patented to another company for barbecue sauce (“Yahoo barbecue sauce” by Ebsco Group). So Yang and Filo devised an idea to make it little different so that the legal barrier could be tackled. Writing “Yahoo!” is different from “Yahoo”, thus they got the patent registration. If you refer to the internet giant yahoo, you have to put the exclamation mark at the end because this is the registered brand name.
Getting back to the question: how important is a brand name? It depends more on what you do with that brand, less on how wonderful it means in the dictionary.