I don't know of any way to change this.
AFAIK the name displayed in the menu bar is the "short name" for the account. The name displayed in Users (and often elsewhere) is the "long name".
The rationale for showing the short name in the menu bar is that it occupies less space in an area that often has very limited display space.
You might see the difference more readily if you create a disposable new account. Give it the long name of "Random Test", and see what the system generates for the short name. Before confirming the account creation, though, change the short name to "ran". After the account is created, log into it, and observe what appears in the menu bar (I expect it will be the short name), vs. what appears at other places. Once you're done, you can delete the account.