Piscivore
Smelling fishy
Technically, if I'm to be a pedantic ass about it (and I am) the more specific name of it is actually an appeal to motive, IMHO.
The line is pretty blurred, but bulverism is basically that you have some personal reason to wish it was true. E.g., as the original example for it "Oh you say that because you are a man."
Whereas appeal to motive is more like, basically, saying "you're dishonest because you have some motive to say/do that." E.g., if I were to say that some review site only gave some product (game, movie, book, take your pick) a better review than another similar one, because the publisher of the first spends more advertising money, that's a straightforward appeal to motive.
Again, the line is pretty blurry. And the exact accusation often left just implied, so it's not clear which it is. And generally I'm often in the wrong myself, when making quick calls about which is which.
So I'm looking at the phrasing in the actual text, "These atheists are usually motivated to redefine the word “atheist” because they want to enlarge the definition of “atheist” to include as many people as possible, or because they perceive it to be an advantage in debates with theists." Sounds to me like a straight up claim that they're telling BS and have a motive to. That's a pretty clear appeal to motive to me.
In fact, IMHO probably you don't get much more clear an indication as when some variant of "motive" actually is spelled out in the text. In this case, "motivated". Ah-ha.
Another indication is that they're not saying it's just some personal belief, but the accusation is basically straight up telling BS for a motive. If I said, for example, "atheists only like to believe that, because otherwise they'd feel like such a lonely minority", now that's bulverism. Then I'm saying basically that it's some irrational personal belief.
You're right, but I was motivated to use the fancy new word I recently learned.