Is it possible to show more information about the booking on PayPal?

No, it is not possible. On PayPal, only the booking number is shown.

There are limits in displaying the service/class/tour name. The name could be too long, or have invalid characters not accepted by PayPal (ex. apostrophes, punctuation, etc), or use accented characters.
Having only the booking number is the safest way to ensure PayPal payments work correctly.

If you want to show more information about a booking, you should use a traditional payment gateway.