There is no requirement as to how you identify WPSs and PQRs other than each document should be uniquely identified.

You can name them Billy, Sally, or Sue if it suits your needs.

Personally, I agree with your proposition to use some rational basis for identifying the welding documents. While a simple serial number for the WPS or PQR is fine when a few are used, I like to read the identifier and understand what it is. I have used the following system for a number of years for my WPSs and it works pretty well for my purposes:

Process, place holder, base metal, base metal, filler metal, letter descriptor. As an example:

GMAP-P1P8F6a

Translation: Gas metal arc welding, pulse transfer - carbon steel welded to austenitic stainless steel, with a F6 filler metal, to ASME (P number used in the identifier), variation “a” to differentiate it from a different WPS denoted by the lower case "b".

I just finished a job where the WPS was supported by several PQRs. I used a similar method of identifying the PQRs. As an example:  PQR: CX GMAP-A/II/B-1000x

Translation: the document is a PQR for a company abbreviated as CX (from the company's name). The welding process was gas metal arc welding using pulse spray transfer. The base metals were Group A (stainless) welded to a Group II (LA steel) using a Group B filler metal and the base metals were 1 inch thick. While I may not know the specific base metal specification used, I do know it is an austenitic stainless steel welded to a low alloy steel using a low carbon austenitic stainless filler metal. The letter "X" just differentiates the PQR from a similar PQR, perhaps PQR: CX-GMAP-A/II/B-375y was similar, but used 3/8 plate and used a different low carbon austenitic filler metal. The base metal groups are found in the body of the WPS or PQR, as is the group of the filler metal. In other words, the designators used can be found in the body of the document.

The system provides more information than using a system with no rational basis such as "WPS-129." I have a refinery as client that used a number system listing 360 plus WPSs starting with 001, 002, 003, … and ending with 368. You have to go through each WPS until you stumbled upon the one you need.  

Any system you adopt is fine as long as it meets your needs. The system should be as intuitive as possible. Some of the value is lost if the system only makes sense to you and not those that have to use it.

As for the length of the designation, it is a matter of how much information you want to provide so the user knows some basic information about the WPS or PQR without reading the entire document.

Best regards – Al