Most metal whistles can be engraved. We have this done at the factory as there is a danger that the plating could be damaged leading to the whistle rusting.
This is expensive but does include an ACME presentation box


If you want to have it done locally cheaper, there are 2 possible solutions. Either have a local engraver put the details on a dog tag and attach this the the whistle ring or buy a polished brass whistle and have a local engraver engrave onto this. As it's brass then it will not rust.