Yes, most travel agency software will let you save a customer's passport and visa details on their profile, so you do not have to ask for the same information every time they travel with you.
The details usually sit on the customer record rather than on a single booking, which means the next time you start a booking for that person the system can fill the passenger form for you. Good software will also hold the document number, the issuing country and the expiry date, and it can warn you when a passport is close to running out before a trip. That saves a lot of back and forth by email, and it cuts down on typing mistakes in names and numbers.
There are limits worth knowing about. Whether those saved details actually reach the airline or the hotel depends on the supplier and on what their API accepts, and some suppliers still want the document entered at the time of booking rather than taken from a stored profile. Holding passport and visa information also makes you responsible for it under the privacy rules of your own country, so you should keep it behind staff permissions, keep it only while you genuinely need it, and tell your customers that you are storing it.
Before you start saving documents for every customer, check what your plan allows, decide who on your team should be able to see this part of the customer record, and make sure your privacy notice says what you keep and for how long.