It's not easy these days to get the domain name you want. I'd say all single word names are already used. Most two word names are used. and most common phrases are also owned already.

But you can find something that works for you. I never have a problem finding a name for my domains, although it takes some thought and testing to find the ones that are still available.

Go to any domain name registrar and they offer a search function. Type in the name you want and they will tell you if it is available or if someone already owns it.

The most frustrating thing for me is to find that some speculator has bought the name I want and wants me to bid on it. I don't . I find another name that is available.

Make a list of words that apply to your site. Think of inventive combinations of three words. Separate the words with a dash ' - ' so that search engines will comprehend the words. But try to find three words that mean something. And be aware that many people do not value names with dashes since they are hard to say. It could lower the value of your domain name while it helps the search engine send traffic there. Since we seldom "say" a domain name, I don't see the negative value of the dash. Mainly they are used as links or written in emails. You have to be the judge of using the dash or not. It is probably just as good to run the words together. 

Take this website as an example. A word plus a phrase. With the two separated by a dash. The first word "Website" means the public and the search engines will know the main subject of this site. The public will see the phrase "doityourselfdoityourself" as a common phrase that everyone understands. When combined with "Website" it is pretty certain what the site is about. So we have humans and search engines both understanding what goes on here.

Try to express something important to your business, blog or customers. Your possibilities are good that three words can be found for any site.

Write down a list of words and go test them on the domain name search. Mark off the ones that are taken. Repeat. Make a collection of available words and then you can choose the one that best fits your site.