If you don't mind me saying- I think having a business name choice dominated by what domain name is available is the wrong way to go.
You're a beauty company- not a internet company selling widgets online
So, your trading name is vastly more important than your domain name. Whatever your web-designer is telling you!
Just choose a simple memorable name, and create a strong brand around it.
The domain isn't going to affect the way people find you (in terms of search engines) and there are ways to relate a domain to ANY business name you choose.
When I was thinking of business names over the last 12 months for a new service I've just launched I thought of (often one word- as they tend to get remembered) words that portray the right message for our industry (in terms of luxury or prestige) - and names that could easily be linked to a strong "brand" in terms of imagery. If you look around the room you're in now- you'll see that's what most succesful brands are. A simple word with a strong image.
Here's the advice from business link-
Do you want the name to reflect what your business does - moving, cleaning, building? Or would something more abstract be suitable?
Would it be a good idea to include your own name?
Do you want a traditional-sounding name, conveying durability and old-fashioned values, or a modern name, suggesting a fresh, innovative approach?
Think about the future - avoid words or phrases that are likely to date quickly.
If you're likely to be trading overseas, check that the name doesn't mean anything inappropriate in the relevant languages.
Think about callers and customers - avoid very long names, strange wordings and unusual spelling.
If you're focusing on the local market for your product or service, think about using the name of the city or town in the business name.
Keep your trading name creative, but your corporate name bland. This will give you the flexibility to develop other brands and trading names in the future.
