The Pantone Matching System (PMS) is a color reproduction standard in which colors all across the spectrum are each identified by a unique name and/or number. The 3 or 4 number code, and indeed the entire name of the spot color is important.
There are a few exceptions, but the PMS naming convention for printing on coated paper is: PANTONE ### C (where ### is the specific number, and “C” designates Coated paper). For uncoated paper, the C is replaced by U. On press, these are exactly the same ink. The C or U designation is there strictly for proofing/previewing and/or conversion purposes so you can more accurately simulate (on screen or in a printed proof) what the ink will look like on coated vs uncoated paper.

The use of PMS allows us to precisely match colors and maintain color consistency throughout the printing process. What makes this possible is the name of the swatch tells the device to look up what color to display or print from its own library.

PANTONE 213 C By Any Other Name…

Design software may allow you to adjust the name and/or appearance of a swatch, but that doesn’t change the rest of the world. If you adjust PANTONE 213 C (a rosy pink) appear green on your computer, it will print pink. The name is what is important. Similarly, if you rename the swatch so that it no longer matches the global library, it will become meaningless. You may understand that “PMS 213”, or “Pantone 213”, or “PANTONE 213 CV” is supposed to be “PANTONE 213 C”, but the computer doesn’t.

Long story short: don’t rename spot swatches, and don’t modify swatch appearance.