Yes, a white label travel portal can let your customers create their own account, sign in later and see the trips they have booked with you. When a booking is made, it is saved against the email address the customer used, so the next time they log in they can see the trip, the names of the travellers and the confirmation details without having to ring your office. Most portals also let them set a password, keep their own contact details up to date and download their ticket or voucher again if they have lost the first copy.
What they are allowed to do once they are inside that account depends on your plan and on the supplier behind each booking. Viewing a trip and printing the paperwork is usually simple. Cancelling or changing a trip from the customer account is a different matter, because the request has to go back to the airline or the hotel, and some suppliers will not accept it unless an agent does it. If you would rather every change came through your team, that part can normally be switched off so the account is there to look at and nothing more.
It is worth thinking about older trips too. Bookings made before you moved to the portal, or ones you typed in by hand, will only show in a customer account if that information was carried across properly, so the history your customers see may start from the day you went live.
Open your portal settings and check whether customer accounts are turned on, then decide whether you want customers changing their own bookings or simply viewing them.