There are normally two ways to name a business. You can have an informative name that helps define what your business offers such as “London Computer Repair” it provides the location but also gives the customer exactly what you offer or something a little less informative but still keeping it relevant like “Rightmove”. The other way to go is picking a random but memorable name such as “Google”. Unless you have a large budget to market a random name it might be worth sticking with a name that tells people about your business. Another form of a random name would be your own name. Many large businesses are just named after the founders names. Random doesn’t mean that the business didn’t have reason behind the name, it just means that it has no relevance when the consumer hears it.
Businesses can range how they are named but a good way to start is to note down what your business is about, for example if you’re wanting to start a photography business then one of the main words would be photo/ photography. You can then come off that and have words like camera, zoom, shot, image. You could use just one word or merge it with another which could be your own name or an adjective such as sweet, professional, expert, quality etc. Ending up with a name like Expert Image.