Looking for a good domain name

Please rethink your idea. You do not want to include a trademark in your domain name. If your site even starts to get popular then Google's lawyers will be on your case quicker than you can create content for the site. I've been hounded by big companies for domains that didn't even include their trademarked words as the domains were too similar. It's simply not worth the risk.

I understand you didn't mean Google as a company, you meant the number (or not?).
But nevertheless it's to popular for perceiving it as a number, so don't bound yourself with Google company (moreover it's not legal).
Think of some other options.

Hi Yosheena,

(1) don't get too caught up with the name itself. Find the function and choose a name that's SEO friendly and brandable

(2) avoid trademarks in your domain name less you want to risk it ceased (at the minimum) later when it gets bigger.

You can use ExploreGoogleNews.com or
DiscoverGoogleNews or
By the way, the 2 names i.e. GoogleNewsToday and GoogleNewsOnline are also very effective names. try to use GoogleNewsOnline , it will be good for SEO results.

If you want to find a good domain name you have many options for that. First of all you wanted to have GoogleNews word in your domain - Not good idea at all. Just by having Google word in your domain name might get you sued due to use of word Google because you don't have permission for using it. So avoid using Google News. You won't increase traffic by having those words because competition is very crazy with those two words since they are used by authority sites and also Google is Google.

As for the options you have about having good domain name, you can always brainstorming like you said. You could start by answering to some questions like "What is my niche", "What is the audience I'm targeting", "What kind of content I should provide", "Who would be my competitors", "What are most useful keywords for my purpose", etc. Based on your answers you can gather them and start generating some domain names.

Another option you have is to pick few words and use domain name generators to generate you a domain name. This is not what I recommend since those kind of domain generators doesn't generate very good domain names.

You can also use Adwords Keyword Tool to find a domain name based on your primary or secondary keywords. Try to have a domain name with 1-3 words and with .com

Hope this helps.

You will be violating trademark offence except you are ready to fight it out(which I doubt) . kindly rethink it and you can try to get domain ideas from namestation(not sure of the extension, but you can google it)

Be very careful about using the name "Google" because of trademark issue.

Dont include the "Google News" name in your domain! I don´t think this will rank good because google will ban you for this AND this is a trademark! So be careful!

I was told by a very wise man that the best thing you can use is your own name as people relate to other people, especially if you are selling anything. Customers want to buy from a person. So just be yourself.