Can my portal sit on my own website address so customers never see another company's name?

Yes, your portal can run on your own website address, and for most agencies that is the normal way to set it up. You point your domain, or a section of it kept aside for booking, at the portal, and from then on your customers see your own name in the address bar and in the confirmation emails that reach them. The booking pages do not need to carry anybody else's name anywhere on them.

Setting this up is a small piece of work that usually happens once, right at the start. You keep ownership of the domain, so you buy it and renew it in your own company name, and a change is made with whoever you bought it from so that the address points to the right place. A security certificate is added at the same time so the address shows as safe in the browser, which matters a great deal when customers are typing card details on those pages.

There are a couple of honest limits worth knowing. While a card payment is going through, your customer may briefly see the address of the bank or payment company handling it, because that page belongs to them and not to you, and the same can happen with a few supplier pages that open in a new window. Whether your emails arrive reliably from your own address also depends on your email provider, so that part may need a small change at their end as well.

If this matters to you, settle on the exact address you want before you launch, and check that the domain is registered in your own company name so that you are never locked out of it later.