Note I’ve written some of the below in vague terms to try to not “give the game away”...
What’s in a (brand) name for the service industries? In the days of the Yellow Pages (what was a major local business directory in dead wood format) having the "right" business name that started with the letter A or multiple A’s e.g. “A Aldershot Plumber” could give you precedence in the listings which were in alphabetical order. Even Steve Jobs chose the name Apple (in part) to be ahead of Atari in the phone book.
Similar (non-alphabetical) principles still apply with Google today. I remember there was a trend a while back to name some (IT-related businesses) “colour / random word” (usally a noun): e.g. “Purple Banana”, “Blue Array” (a real SEO agency) etc as a "brand". These names might be memorable (sometimes) and help people recall you / find you when searching by name; but to businesses that are “internet first” there are few other advantages from what I see. Were these company names inspired by Seth Godin?
Key words are important to search engines - I would say that the “(irrelevant) colour name/ (irrelevant) random noun”-type of brand name is an actual disadvantage today in terms of Search Engine Optimisation for many (services and arguably some ecommerce) businesses…
In a word where the Yellow Pages (and Yell .com) has been superceded by search engines like Google, your business' (brand) name remains very important, but this is no longer simple alphabetics. Your brand (naming) strategy (and the various aspects of digital marketing / business that may be dictated by it including for Shopify websites their store name) is integral to a holistic digital marketing strategy. Keyword research relating to your business is the starting point...
I’ve seen many (service industry) businesses in competitive markets such as EPOS, construction etc with arguably irrelevant brand names (which have not been designed as an integral part of their wider digital marketing strategies) being outperformed in Google organic search by competitors with a “does what it says on the tin” accidental brand (naming) strategy whom it appears have not ever having done much / any 'SEO’ activity at all . This is often in the face of much larger competitors with a good (but not fully integrated) digital marketing strategy ‘doing a lot of SEO’.
I had a client who changed their domain name (and at the same time changed their trading style / business name on the Google Map - of which I was not informed of at all) - this appears to have dramatically affected their visibility in Google Map listings (integrated into search results) for many core key phrases in the London area and beyond.
If you need help with (re-)branding (maybe as part of a holistic digital marketing strategy review) get in touch.