Bar my perverse and entirely irrational aversion to Shakespeare, I don't really give a damn what name a bit of fishing kit carries. However, I don't generally operate in the budget price ranges. If I genuinely believed that I could get a Cormoran version of a top end Daiwa, for a much lower price, I'd happily buy it. However, the reality is that this kind of thing rarely happens. The multiple brand companies have their flagship brands, and that's where their latest technology and innovations end up first. Yes, you might find a budget Daiwa rod with Cormoran on it at a lower price, but you aren't likely to find an Airity or Tournament RS with Cormoran branding any time soon.
Daiwa and Cormoran are effectively the same company, but Cormoran aren't a big presence in the UK.
Hardy, Greys and Chub were offshoot brands of the same company. Now they are part of an even bigger umbrella company with even more brands, Pure Fishing. They have Mitchell, Shakespeare, Abu, and others, as well as Hardy, Greys and Chub.
Zebco Europe have multiple brands, some of which aren't overly familiar, but Browning Fishing is one of theirs.
Preston Innovations has their main brand as well as Korum (their specialist arm) and Avid (carp).
Fox have carp, predator and specialist brands. They used to have Fox Match too, but that's been rebranded as Matrix.
Drennan operate ESP as their carp brand.
Korda now has their own match fishing brand, Guru.
Shimano are actually Shimano Normark UK. They operate numerous sub brands such as Dynamite Baits, G-Loomis, Rapala, PowerPro, ACE, Sufix and Storm. Weirdly , they've done nothing much with the Normark name since they bought it.
The reality is that there aren't actually that many entirely discrete brands out there. It's entirely possible for a local shop to effectively have almost all its stock come from just a couple of companies.