Pre-school? or preschool? and why?

[Lemonsole]

My gut instinct is for the former, when using it with another noun, eg. pre-school education.

But is the noun, i.e. St Pedant's Preschool hyphen-less? Or St Pedant's Pre-school?

Please help! Our new sweatshirts are going soon to the printers, and we want the logo (a) to be correct, and (b) to be able to explain why it is so.

Many thanks.

I would use the hyphen.
I hate the term pre-school (or preschool) anyway. What happened to the nursery class?