Can I find an old booking in the software if my customer only remembers their name and roughly when they travelled?

Yes, that is usually enough to find it. Travel agency software keeps a record of every booking made through it, and those records can be searched on the details you are most likely to have to hand, such as the passenger name, the travel dates, the destination, the staff member who made the booking, or the booking reference if the customer still has their paperwork. If you are not sure how the name was spelled, searching on the first few letters will normally bring up a short list to choose from, along with any other trips the same person has booked with you.

When the customer is vague about dates, the better approach is to search a range of dates rather than one exact day, then narrow the list down by destination or by whether the booking was completed or cancelled. Bookings you entered by hand, for things you arranged outside the system, are stored in the same place and come up in the same search, so you do not have to look in two places.

There are honest limits worth knowing. The software can only find what it holds, so trips arranged before you started using it will only appear if those older records were brought across when you set up. On top of that, a supplier may no longer hold live details for a reservation that travelled a long time ago, so you might see your own record of it while still needing to contact the supplier directly for anything current, and how far back that reaches varies by supplier. The search filters available to you can also depend on your plan.

The next time a customer calls with only a name, try a partial name search across a wide date range, and have a look at which filters your own setup gives you so you know what you can narrow by.