Hi Maureen,
Thank you for bringing your question to the forum. I have a few of thoughts on this:
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First of all, folks are very unlikely to be seeking your business or your services by entering a phone number. So, I would call this concern a very low priority.
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However, here's what I think may be going on, as I was unable to immediately find anything connecting your phone number with your competitor (something may exist somewhere, but you'd need to hunt to find it if it does): I suspect Google is confused. The similarity in business names and domain names is leading Google to be uncertain about the identity of the business connected with that phone number. Because your competitor has earned more links and has a higher Domain Authority than your business, Google (in their uncertainty) is bringing their SERP entry up above yours. It's certainly weird behavior on their part (if, indeed, there is no asset connecting your number with their business hiding somewhere). But, that's my best guess. Somewhere in Google's system, they are confused about the identities of the two businesses and are conflating them with the same phone number in your phone number search.
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What to do about this? According to Moz, your numbers stack up against your competitor's like this:
Them:
Page Authority: 25 ; Domain Authority: 19 ; Links: 911
You:
Page Authority: 5 ; Domain Authority: 3 ; Links: 2
As these numbers indicate, your brand is behind in building overall authority, and this is why I strongly suspect that Google is allowing this business to get into the mix of your search engine results because they aren't quite sure whether the competitor's stronger presence is actually a better version of your own business. This is my theory, anyway, and if correct, what you need to do is build up the authority of your domain so that it is firmly associated in Google's mind with your phone number.
You need more links, in short, and, as others have mentioned here, you may well need to start building out your citation set. Moz Local would be our home-grown solution for a UK business like yours needing to ensure that its local platform and directory listings are accurate and complete . You can learn more about it here: https://moz.com/products/local
- Back to the beginning of this: it's unlikely that your brand is being harmed much (if at all) by what you've noticed regarding the phone number. People just don't typically search for brands or services by phone number. But, there is a good chance that your low authority is causing you to be outranked for the keywords that people DO search for in trying to access services like yours. And, what you've noticed is actually a good indicator that Google currently lacks confidence in the information they have about your business. That definitely matters, and so, the best way to build up Google's confidence is to grow your authority. I recommend that you put priority focus on both links and local business listings and that should be a smart start to making Google more confident about who your business is (and who it isn't!).
Hope this helps!