What you are really asking is whether the designer initials are part of the master hub or punched into the working die. They are part of the master hub.
The mint changed the process, although I don't remember the year. Certainly into the 20th century, the master hub was used year over year and so the date and mintmark were left off.
In the early days of the mint (1790s) the master hub would just be the central design element (the bust of liberty or the eagle) and then the lettering would be added to the working dies by hand. This caused each working die to be slightly different (the master hub elements would also be touched up by hand). The punches would have slightly different alignment, be rotated or even positioned slightly differently.
This is why coins up to the 1860s or so are collected by die marriages, in part because it's easy to see and trace the unique dies. You see the same thing with
Morgan dollars, where the tiny touch-ups and cracks of the dies make it possible to trace (VAMworld is the canonical site).
This is also why you see things such as 1939
Jefferson nickels with the "reverse of 1939", either a left over / partly used '39 die was used into the new year or the die was made from the old hub.
Today it's all CNC work, so the concept of the master hub is different, if they even use one, it's as a master to be scanned, scaled, cleaned up on the computer and then used to cut the working dies. Watch one of the newer mint videos to see the process from the plaster master.
-----Burton
50+ year / Life / Emeritus
ANA member (joined 12/1/1973)
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https://www.sampleslabs.info/