Will the confirmation emails my customers get show my company name or the software company's name?

Yes, the emails your customers receive carry your own company name and logo, not anyone else's. A white label portal is built so everything the traveller sees belongs to your brand, and that includes the booking confirmation, the voucher and the payment receipt. Your logo sits at the top, your company name and contact details sit in the footer, and the sender name is set to your business so the message reads as if it came straight from you.

The one part that usually needs a little setup is the address the mail is actually sent from. For customers to see your own domain as the sender, a few records need adding to your domain so that mail providers trust messages sent on your behalf. Your domain host can do that quickly, and until it is done the emails may still go out from a neutral address with your branding inside. Whether a fully custom sending address is included can depend on your plan, so it is worth checking.

The honest limit is on documents a supplier issues directly. An airline e-ticket is produced by the airline or the system behind the fare, so it keeps the airline's own layout, and some hotel vouchers show the supplier reference alongside yours. You can send these inside your own branded email, but the wording printed on them is not something you can rewrite.

The simplest next step is to make a test booking, read the confirmation as a customer would, and then tell us what to change in the logo, sender name and footer wording, and whether you want your own sending domain set up to match your website.