Companies house is just for Limited companies. It doesn't mean you can't have the name and it's not where you register one.
You need to trademark a name if you want it exclusively to use in your industry. It's not badly priced but it can take a while to all go through and you need the money to defend it should someone breach it. Lots of info here - https://www.gov.uk/topic/intellectual-property/trade-marks
You'll need to search the register in the class you want to register in to check it's not already taken.
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