If you could then there would only be 1 coffee shop or 1 firm of solicitors
You can however protect the expression of an idea
This can be done through a registered trade mark (for the name), a registered design (for the design) and copyright (for the text/ website etc).
Creating a strong reputation in a name and design and then protecting the same is the best way of ensuring that even though you cannot protect an idea, the consumer comes to you first as the pioneer of a particular service/ goods