Several things to consider when coming up with your product's brand identity:
1) Who is your customer? That will drive the look and feel, as well as the language of your brand.
2) Who are you? If at a gut level, you and your company(employees) are rednecks making the highest quality broadheads for elk hunting, you aren't going to button up your brand in a shirt and tie or develop an artsy-fartsy website. (See Duck Dynasty)
3) What specific aspects of your product and/or service are different than the rest of the market offerings? Ie. Why are you special?
These 3 questions, answered candidly, begin to make up your brand story.
The most powerful brands have learned that their messaging, packaging, sales process and customer experience delivery is less about what their product or service DOES, and more about how it makes the customer or user FEEL.
Branding a product or service is about carefully crafting a story(or a promise), that you are confident you can deliver on once they choose to buy.
In other words, branding is the discipline of aligning what you say about your product, service, team... with what customers actually get on the back-end.
Once you get really clear on these big picture questions, then the tactical stuff becomes rather easy (what should our website look like, colors, advertising channels, promotional pricing, referral programs, warranty language, etc, etc, etc.)
Of course you may be smart to hire a specialist to help you brainstorm and execute on this stuff- but the actual decision making becomes pretty obvious: which option in front of us best reflects who we are?
Make a word list, grab a thesaurus and a Latin dictionary, pour out your Scrabble tiles. Put on some music. Tear pictures out of magazines. Doodle. List every idea, edit later. Generate hundreds of ideas. Pick your favorites - a bunch of favorites. Draw the label as you'd see it on the shelf. Try it out as an email address. Answer the phone with it, see if the caller understands what you said. Screen the ones you like most for availability. Pick from the survivors. That's all mostly for the "name" part of the brand - a "brand" is something bigger, actually, but I guessed from your question that you were asking about the product name itself. Give me a call if you need some help with any of the "verbal" part of your brand strategy.
The best way to come up a brand is to brainstorm... Don't settle on the first thing that comes to mind find your niche ask yourself what you are good at... Who is your customer... I have a brainstorming questionnaire that helps me with the process it helps narrow the funnel.
This is a bit unconventional, but it's what I call the "Can A Kid Remember and Spell It Test"...
Once you have a name you like, find a kid who is around 3rd-5th grade and tell them the name, and see if they can repeat it back, and spell it.
The most important element of a brand name is that its easy to communicate via word of mouth, and once someone hears about you, they can easily find you.
So, if a kid can remember and spell it, you are good... if not, start over...
The second best piece of advice is DONT FALL IN LOVE WITH A NAME!!! Ego is a business killer, and I have seen so many companies come up with a clever name and fall in love with it, even if its bad for their business.