In my opinion, if a given brand of wire is written in the Welding Procedure Specification, it's that brand that must be used, precluding any other one. This is because for some reason (and it better be a good one), who wrote the WPS doesn't trust other brands.
I don't know your particular case, but it must be one of the following two:
1. You're writing a WPS for a client. In this case, it's highly advisable that you get your client's approval about specifying a particular brand.
2. You're going to be qualified according to a WPS that specifies a particular brand and you would prefer to use another one. In this case, it's up to you to convince your client (or your boss) to use the brand you wish, which isn't the specified one. One way to do this is to run the tests using your preferred  brand, and if the results are OK, this demonstrates that your preferred brand is also OK.
Giovanni S. Crisi
Sao Paulo - Brazil  

There are times when it is prudent to include a particular manufacturer and brand name of a specific electrode. When that is the case, write the specific brand name where classification would normally be placed.

This is where I start my rant if you care to call it that. I do not use the WPS format included in AWS, ASME, or other welding standards because they don't provide sufficient space to list all the information the welder needs or would like to see included in a WPS. I generate my forms using a word processor and I use the "Table" function to produce the basic form. This allows me the latitude to add or delete information as necessary. In this case I add two entries after "electrode classification". You can guess what they are, of course, an entry for "Manufacturer" and another for "Brand Name/Trade name".

It is generally accepted that if a specific manufacturer and/or trade name/brand name is listed, their use is mandatory. There are plenty of reasons for the welder to be directed to one specific electrode over another even when they meet the same electrode specification and classification. For example; several manufacturers produce several different E7018 electrodes, each with specific alloy compositions. While each electrode meets the requirements for the E7018 classification, the alloys contained in the covering (composition) can results in different chemistries in the weld deposit while still having the required tensile strength, ductility, etc.

In my case, I often develop repair procedures for existing (read that as "old") equipment. Many times the machines are steel castings. When I develop a repair procedure I verify the chemistry (by analysis) and look at several elements that may cause problems. Carbon, sulfur, phosphorus are problem children when considering welding. I know that if the carbon and/or carbon equivalency is high, I have to increase preheat. If sulfur is high, I know I need to use an electrode that has "high" manganese to counter the sulfur. That's when I compare the deposit chemistries of several different electrodes. Do I need to use low hydrogen type electrodes? Do I need to minimize the carbon content? Do I need to maximize the manganese content? Based on the answers to these (and other questions) I select the best electrode for the application. When it is necessary and when it makes a difference, I list a specific manufacturer and brand name / trade name in the WPS. I accept no substitution unless I've had an opportunity to verify the substitute is at least as "good" as the electrode I listed. 

Best regards – Al