I was thinking about this as I was digging into a uniquely-packaged container of Boursin cheese. Not only is the cheese delicious, but the foil wrapping is unique. When you think of Boursin, you think of the packaging as much as the flavour of the cheese itself. Their uniqueness is built into their advertising as well. That is what you need to think about when building recognition for your company.
Whatever business you are engaged in, there is competition. If you have a business with no competitors, I would love to hear about it. But I digress. You have competition; I have competition; we all have competition. Accept that as a fact and then see how you can tweak that one little part of your identity somewhere to make you stand out.
Maybe it is how you promote yourself; maybe it is that one shockingly unique colour in your logo, maybe it is the one way you create a service perk far and beyond what anyone else can offer.
Create something so that whenever your company name is mentioned, clients and potential clients have a prevailing thought that comes to mind. Meld the combination of the company name and that one "sweet spot" of uniqueness and you have a unique identity that will put you beyond a lot of your competition. Yes, the competition will be there because that is a fact of business. However, dominating the market is your goal and you can't do that if you are just like everyone else.