I agree with Shane.
If the WPS lists the brandname of a specific electrode, it is still a nonessential variable for work that does not require notch toughness per D1.1. The WPS can be revised to drop the brandname or change the brandname. If the brandname is listed, the welder has to use it for production. He does not have to requalify by testing if the WPS is revised or he welds using a different WPS as long as the F number of the "new" electrode is covered by his/her initial performance test. In other words, if the welder used E7018 for the performance test, he/she is qualified for F1, F2, F3, or F4. The welder can use any electrode provided the new WPS lists one of the covered electrodes falling into one of the F number groups for which the welder is qualified.
For example; The welder qualifies with an E6010 covered electrode, it is an F3 electrode, it qualifies the welder for any F1, F2, or F3 electrode. If the WPS lists ACME Super Low-Hi E7024, the welder is qualified to use it because it is a F1 electrode. If the WPS is revised and drops the brandname and simply lists E7024 the welder is still qualified to use any F1, F2, or F3 electrode. However, the welder is not qualified for E7018 because it is an F4.
As a recap; just because a welding variable is listed on the WPS, it doesn't mean that variable becomes an essential variable. A change to an essential variable means the WPS and/or welder has to be requalified. In this case, except for welds meeting notch toughness requirements, the brandname of the covered electrode is a nonessential variable meaning the WPS can be revised to include a different brandname or drop it all together. No additional testing is required.
Best regards - Al