It doesn't work for me. It's like naming him Port or Preserve. It just doesn't seem like a name to me. I didn't check the web to see if it's a legitimate name; I'm just giving you my initial impression.
I agree with PPs. When I see Haven, I think of the word not a persons name. There are some baby names sites that list this as a legitimate name but it's listed as a girls name, not a boys.
Re: Haven
I think girl, and not really a name.
I like Hayden for a boy
It's not a name. Other H names: Hugh, Henry, Howard (Howie), Harvey.