Despite running a site selling domain names, I’m a big fan of trying to find a “free” domain first. By free I mean either one that costs a normal registration fee or is dropping. I’ve found decent free domains for several recent ventures, and if you’ve done the legwork you’ll feel a lot more comfortable paying for a domain if that’s the route you’d like to go. Of course, if your time is valuable enough then I don’t object impulse purchases.
I like to divide the search for a name into several steps.

First: Try to identify words and concepts associated with the business you are trying to enter.
I recently started a site for a bankruptcy related product which meant I needed to include the keyword bankruptcy and there weren’t other good options. Other fields may have numerous words legitimately associated with them such as wealth management; legacy, protection, guidance, and many others. I recommend looking at industry directories and thesaurus to develop options.
Words associated with qualities and industries also bring their association to roots. For example lega combined with many ending would be brandable but still evocative of the original concept. Legatus Group sounds respectable and is an actual financial planning company.
Second: Start mixing things around
Keep in mind the common endings that frequently make a sensible word; ly, sy, a, io, ia, us, om, and o. You can probably think of some more. I would start by appending these to the end of the words you started in step 1.
Words associated with qualities and industries also bring their association to roots. For example lega combined with many ending would be brandable but still evocative of the original concept. Legatus Group sounds respectable and is an actual financial planning company so good that several variations are taken.
To check availability you can run a bulk list through Godaddy, which is an okay registrar and can generate some suggestions that aren’t too bad if the name isn’t available.
Third: Try the generators.
I wouldn’t spend too long on step two. There are a number of domain generators out there that work quite well.
The one I usually start with is lean domain search which displays whatever you type in with whatever is available out of a list of the most popular words and endings of registered domains. I found bankruptcybase.com using this software and bingeout.com was also named using lean.
I like lean because it allows you to focus on real combinations of words. I personally don’t like to go over two words with the exception of the use of small prepositions in the middle(my, go, etc.), like foundmyfitness. Prepositions sound cheesy but running my+a related keyword through lean can come up with some catchy sounding phrases.
Fourth: Try to Catch Something.
Catching a dropping domain will in all likelihood cost you more than the registration fee. There might even be an auction but typically you’d probably pay 5-35% of what you would pay on a marketplace. It’s a great way of finding good domains on the cheap. Unfortunately, only a limited number of good ones drop so choices can be limited. I buy domains weekly and accumulate an inventory of good one.
It’s also costly in both time and you’ll need a drop tool. I use domcop.com. Basically you just enter your constraints in the advanced search and you’ll see all the domains available. Be sure to enter a max price of 70 so you only get true dropping domains.
Dropping domains come in two categories. Pre-drop auctions at the registrar where the domains are registered. These can be fairly reliable. I would not bid on a name until the last minute. People search for domains with bids so they don’t have to find the good ones. I’ve started many bidding wars.
True drops involve having the domain lapse and then dropcatch services like dropcatch.com, snapnames, or pool.com will send in automated requests to register the name. First one to get it wins. If the winner has multiple bidders then they will conduct an auction.
So that’s a quick guide to securing a free domain name. Try to do a domain clearance and think about trademarks before you register a domain so you don’t run into problems later.