You can have multiple trading as names under your sole trader business, so you don’t necessarily need to register a separate company unless you have a specific reason to do so.
A limited company does offer benefits, particularly when it comes to tax. Once you earn over £12,570 per year (your personal allowance), a limited company lets you take dividends, which are taxed at a lower rate than wages. However, running a limited company comes with extra costs—if you already use an accountant, you’ll likely need one for a limited company, and their fees can be higher (often upwards of £1k per year). It’s worth running the numbers to see if it makes financial sense.
Regarding working from home, most people can get away with it, but if you rent, some tenancy agreements require you to inform your landlord. Likewise, some mortgage agreements ask you to notify them if you're running a business from home.
Trademarking—if you’ve got a strong name and think others might copy it, then yes, it’s worth considering, especially if you want to sell the business later. But it can be pricey, so weigh up whether it’s necessary at this stage.
That said, I’d ask why you prefer to keep the product separate from your coaching. As a professional in your industry, your story could be a huge selling point. Think about sports professionals who have launched products—they don’t distance themselves; they use their experience to add credibility. When it comes to marketing, brands that show the person behind the product tend to perform better than those hiding behind a logo. People buy from people they trust, so it might be worth leaning into your expertise rather than away from it.