This is a problem that crops up a lot in business.
You are going to try something new in the market, so you need a name. It is one of the first problems you will have in your business. It crops up, again and again, e.g. you are running a lotto synidicate this week, you want an online webstore, say you are going to start a new product line selling vitamin pills in the shop, etc well what are you going to call it?
I read an interesting article on facebook, by a professional who for a living advises people on what to name their business ventures. I am sure he charges thousands of dollars for doing it, but he sparked a lot of peoples interest on the subject.
Here are my steps for doing a naming and some observations
Write down some ideas that identify your proposed products, some immediate ideas on a business name, eg a butcher shop on North Rd might think of "North Rd Butcher", competitors names - it worked for them why not for you, etc. Now several websites that can help you. My current favourite is here but there are many more sites so pick the one you like. Now put into the search box one by one these ideas and flick through the options and its proposed names and write down the ones you want. I am sure there are many good ideas here.
For a website, try and link it to your actual name if possible. Your new website should feed the shop, and your shop should feed the new website. Why re-invent the wheel, so use the resources you have.
Now talk it over with people but trust your judgement, as you will have to live with the name. So pick a name that communicates your business.
Shorten the proposed name and see if you like it because, over time, it is the short name that you and everyone else will be using. Invariably I do not tell people I work for POS Solutions. I say POS if they ask its Point of Sale.
There is no excuse not to check the proposed names and grammar in google translate with several languages that will be used by the locals. As you do not want every few days someone telling you cafe name means this "*gh^%@!" in their language or your French grammar is wrong. At best, you look unprofessional, at worst it can be pretty bad. I had a client who discovered that his business name based on the street he was on, translated into English meant something like a castrated pig store which is to Eastern Europeans particularly nasty. The guy that named the street, I am sure had a really good laugh when the council adopted it. So I would strongly suggest that you check your proposed name with several languages. At least Mandarin, Arabic, Cantonese, Vietnamese, Greek and Italian.
It is worth taking some time as a good business name can go a long way to making your business and/or website.
Note: Sometimes you get only a limited choice. For example, when we were starting up, I wanted POS (Point of Sale) Software because that is what we were marketing. My partner wanted Positive Solutions because he was a positive fellow and we had a Point of Sale Solution, so I compromised it and made it POS Solutions. Everyone liked it, so we ran with that.