I pronounce this name with two syllables, ev-ritt. I prefer it that way and it sounds better when saying it with my Mid-American accent. We are naming our first boy this and nicknaming him Rett. It is very gentlemenly, yet not pompous which I like.
Everett was my great-grandfather's name; when I told one of my friends this, she thought it sounded backwoodsy (I don't). I like the sound of it, but I'm not too fond of the meaning.
When I was little, I thought this name was very trashy because this really trashy metalhead guy in my extended family was named Everett. But then, I volunteered at a feline clinic/shelter and while I was there I met the sweetest cat named Everett. That cat completely changed my impression of this name.
I've a friend with this name. For him, the correct pronunciation was EV-rit (two syllables). However. I have seen this name pronounced EV-ə-rit, EV-rit, and even EV-ər-rit. [noted -ed]
Former painter Thomas Kinkade's youngest daughter is named this, presumably after the painter Everett Shinn. IMO unless this is a family name, I think it is really terrible on girls. Thankfully it's still predominantly masculine. We've already lost Addison, Ashley, Taylor, Mackenzie, and countless others to the female gender; we don't need to lose Everett, as well.