Oh, there are many. It's family-specific in the US.
Nukky-from a brand name; unfortunately, this is also a silly nickname for sex; binky-although some people use that for blanket; dummy-but this can also be an epithet for "stupid"; passy-spelling it paccy looks funny.
A neighbor. long ago, had a nanny from an unnamed country. Said nanny was determined to master English. She refused to use baby talk with the neighbor's child, who thus was offered the object this way: Would Edward like his rubber nipple now?
You sure you weren't thinking of "equalizer?" Oh wait, it just came to me-- the Peacemaker. And I'm sitting here explaining a bit of your wordplay.
Yes, pacifier is very well-established in AE, it's the default term. Why in the hell can't people just let their babies cry themselves out now and then? It's like getting the RPMs up and blasting the crud out of their cylinders.
There seem to be many words for this object! What do you call it in your corner of the globe?
Around here (Abbotsford, BC, Canada) we call it a 'soother' if it's shaped like a nipple, or a teething ring if it's ring-shaped... I think my grandmother calls it a pacifier, is that representative of southern BE?
We called it a (I don't know how to spell this.) tootcher. The u sounds like the oo in foot. I think it is a low German word, or an Anglicised low German word. I heard someone else call it a boober. I've also heard "dry cow".
Pacifier is the generic term that I am familiar with.