I talk with a fair number of start-up companies and I'm always able to tell who chose the company name. Not the specific person who chose the name, but whether or not the name originated from within a marketing function or a technical function. I can also usually tell if it's a second or third generation name.
The technology function tends to love names that are cleverly descriptive of what their underlying technology is or how it functions. Sometimes the names are difficult to say or remember, but that doesn't matter. The more descriptive the better, and if it's disguised in some type of word play that's even better.
The marketing function tends to love names that connect the company's product to current popular trends. They also seem to love names that are enigmatic enough to allow meaning to be built into them through use.
And then there are the names that are descriptive of a company's benefits. Usually simple, and often indirectly referenced, these names reinforce what I will be buying into when I choose their products. In my very small sample size, I've noticed that these names are often second or third generation names of these companies. There are often stories about how someone realizes that what a technology does for people is more interesting than the technology itself. Or they realize that it's more important to differentiate from the sea of My- or i- products and companies, than to show a connection to them. The key is that the name becomes relevant to the consumer, rather than relevant to a technology, internal preference, or discipline the consumer may not know exists.
This is the way to enable the consumer to influence your business right down to the name. It's not about asking them to choose their preference from a set of choices. It's about understanding what you provide that is relevent to them, and reinforcing that value in the name.