The LaserWriter Pro 810 User's Guide is correct. For clarification, the last paragraph of page 43 in the manual states:
IMPORTANT: The LaserWriter Utility will let you create a name up to 31 characters when you are using the printer via the serial or LocalTalk port, and a name up to 16 characters when you are using the printer via the Ethernet port. (The printer can have two different names: one for the LocalTalk connection and one for the Ethernet connection.)
The reasoning behind only supporting 16 characters for the Ethernet printer name is due to the 810's virtual printer technology (only applicable on the printer's Ethernet interface). Since there can be a total of 64 different virtual printers, the data structure keeping track of the names could only support a 16 character string. In other words, there was only enough memory to store 16 x 64 characters.