Head is better than Director.
But, understand what it really probably is, is a hedge. It’s a hedge you may not make it to VP. You may not really be able to pull it off. You may need to be topped in the next 12 months.
Not always. Some companies like “Head of” to feel less structured, less stuffy.
But usually, it’s a hedge.
You’ll have to earn it.
But that’s OK. You should have to earn it. Really, you always have to earn it.
In any event, my suggestion is to do what makes the CEO comfortable. This is what she wants to do. I’d just do that. And revisit it in 4–5 months once you’ve crushed it.
More here: Don’t Ever Make Anyone “Head of Sales/Marketing/Engineering/Whatever” in SaaS