The most important thing you need to remember is not to make sure your business name is not taken yet. There are names that are copyrighted and you will not be able to use the name. Keep in mind that names can be used even if there is a company with the same name. Depending on the state you live in, you may be able to use a name such as "Sunshine Bakery" even if a company such as "Sunshine Tanning" exists. As long as both businesses are in different industries that should be allowed.

As for naming the company, use your imagination! Think of ten things that are important to your business and see if you can capture those things in one or two words. Good business names might not have anything to do with the business itself but more as a general name that works. The word sunshine would be a good name for a variety of businesses: Sunshine Bakery, Sunshine Tanning, Sunshine Beachwear, etc.

Naming the business is not so easy, but sometimes companies don't actually know what they got like Apple.
Apple , just imagine a name of cell phone maker and it related company. While considering the name they actually not know where to go, what to choose but when they got name 'Apple' they started creating associations with that name.
Most of the companies have their names with the name of owner like 'Disney, Ford, Nestle etc. So it depends what you choose and most importantly how you utilize this name.
While selecting business name you have to consider following things:

Name should be easy to recall and easy to spell and understandable for every language.
You can go for ownership or choose unique, abstract name or related to business category. But whatever you select, then only focus on it and start developing good image
You can go market analysis and see what customers want and how they see a new name in the particular category.
As you mention that, you start expansion in new product line, so you can do family branding, attach a unique name with your existing corporate name if has any.
Your business name should represent three or at least one from the following:
Your area of business,
Core benefit
Target market
You can add one of these in your slogan - positioning statement

Develop alternative at least 3-5 and then it is very easy for you to select one of them.
Involve your employees and loyal customers - stakeholders and listen their ideas in the form of brainstorming. you can do, just think differently

Go beyond, think longterm, no strategy works best if implemented poorly. So develop a vision and set goals then choose the name accordingly.
Thanks
http://thinking-brands.blogspot.com

These are the things worth considering when naming your business:
*research your business name so that you will know if the name you have chose is already taken or not. You can use the internet for your research. You can do a general research for your business name on a search engine. By doing so, you will know if the name you and your colleague have chose is taken or not. You can also do a search through your Secretary of State.
Before you settle on a final name have some different variations so that you will not be disappointed if one of them is taken and you have an option.
Another thing to consider is trademark infringement. Make sure that you don't choose a similar name of another corporation and sell the same or similar product with that corporation. Avoid causing confusion to customers and trademark infringement lawsuit by other companies by creating a unique business name.

Source:
http://business-law.freeadvice.com/business-law/starting_a_business/name-corporation-3.htm