I have a B3 here that someone traded in and it does have a very small serial number on the handle, ‘1695’ by the looks of things.
Aldred does
The blank bat I got off eBay that was apparently a Hawk has one, it looks to have been stamped in then coloured with biro! More interestingly it was bound with blue twine...
Yep Aldred does on all his batsB3 do on the twine