Thanks, cptbilly!
And this is indeed the solution to this "old" puzzle. Ch. Petersen.
It's just that on the medals that I have, his signature is complete. Often medallists have only initials on the first medals, and then they switch to a full signature. See, for example, J.R. Sinnock. But some artists use both signature options.
I have never heard of a bust of Wilson by Petersen that is so similar to the photos. But having set a search for medals by Ch. Petersen, I found this medal, where the signature is exactly what I assumed.
Iowa State College Alumni Medallion
Petersen's mark which is a capitol "CP" inside an oblong box.


Thanks again. We can correct the information in the catalogs!