You say the tyres are 'no name' but sometimes its a case of 'not so well known or widely advertised' . Most of the historically well known 'premium brand' tyre manufacturers also own a few lesser known brands and make them in the same factory, along side their premium brand tyres. The extra cost of their best known brand partly goes on extra advertising, motorsport sponsorship, and simply because buyers will pay more for the history and hype. . They get to sell some at premium prices and also a share of the more budget conscious market. Win Win.
Here is an example. Tigar Brand tyres made in Serbia. Tempted? . But Tigar (not tiger) brand is 100% owned by Michelin and both brands (and some others) are made in the same factory. I have driven past it. Looks very modern and state of the art. Not saying I would buy Tigar tyres, but would Michelin deliberately make really rubbish tyres ?
Also sometimes a high quality tyre that has a very good reputation in Asia for instance is relatively unknown to the general public in Europe, or the uk in particular. Sometimes these are sold at a budget price to promote their recognition and reputation in new markets. I can remember when some top Asian Brands such as Yokohama ,Bridgestone etc were virtually unknown here.
There are some crap budget tyres of course. But it might be worth giving yours a chance, and researching them on line. You might be pleasantly surprised.