I would argue that Nintendo is the strongest brand name in the industry, but I think the fact that when somebody mentions the playstation, they are talking about a console specifically, says alot about how well Sony's strategy of keeping the playstation brand name is doing for them. EDIT: I would say that if Nintendo kept the Wii name in some shape or form next generation, it'll easily eclipse the potentially 4 generations (including PS4) worth of brand name establishment that Sony has done.
Also, I think you're contradicting yourself a little. The fact that even with the playstation brand name (assuming it's the strongest), the PS3 is still stuck in 3rd by at least 8 million (Wii is obviously higher) would suggest it's not that strong. (That is of course flawed because I don't factor things in like price. But using the Ipod as an example, there are definitely cheaper and better alternatives out there, but it still reigns supreme in the Mp3 market.)
A better comparison would have been the playstation brand is the apple mac of the video game industry, it's a well known brand but there's something else thats definitely ahead of it (PC's with windows).