Should I run several niches under one brand, and do I need a separate website for each niche?
It depends on how you position your agency.
If you niche down, start with one niche. A narrow niche and one dialed-in offer make it quicker to get results, keep clients and scale, because you repeat the same process. Targeting several niches multiplies your work, with a site, landing page, marketing emails and lead magnet for each, and spreading across many niches dilutes your specialty. Votel recommends a simple, clean brand where nobody can mistake what it does and who it serves, even with the niche in the brand name (for example HVAC Solutions R Us). Opinions vary, so choose what suits you.
If you do target several niches, make a separate landing page for each so you speak directly to that ideal client, and send each niche's ads to its own page. If the niches share a category, such as contractors or home services, one site can speak to all of them with shared language like more booked jobs, followed by the types of businesses you work with. If the brand is your agency, use a page on your agency domain or a subdomain (for example cleaning.yourdomain.com). If you want separate brands, use a separate site and domain.
If you are a local agency working with businesses of all shapes and sizes, keep everything under one brand and one domain, for example a local marketing agency serving your area, and keep adding example industries as you get clients. You do not want ten niche websites. Expect more setup work per client at the start, and over time build a snapshot for each niche you serve. One agency typically has one Google Business Profile.
Technically, all your niches can run from the same agency account. You have different websites, agents and forms for each niche, while all your contacts, customers and leads stay in the same account and CRM. Build on your main account, then push each setup to client sub-accounts with snapshots.