Name your own price? Hah!!!
There are two possibilities:
1. They mean it
2. They dont really mean it.
If (1) they mean it, then they are silly, particularly if you are a newbie. I wouldnt even let established authors set their price. Established publishers know their costs and know what they can afford. If the author wants too much, and I cant afford it, then we cant do the project. Its as simple as that. No hard feelings. I didnt go into business to lose money on a project.
If (2) they dont really mean it, then they are using the age old negotiation tactic of "making the other guy open", meaning they want to see what you think you are worth and negotiate down from there. They want you to set the upper limit, relying on the time honored principle that people are polite and dont like to ask for too much and will usually sell themselves short without them even having to do it to you. Personally, I like to be up front about rates. I always open so the author sees I am up front. Thats because I know what my costs are.
Ask for 5 cents a word then and see what they say.
I will tell you that any d20 company that wants to stay afloat will pay anywhere from 0.5 cents a word to 4 cents a word (with the latter being rare and for only the most senior author on the most important product). Getting 2 cents a word these days is pretty good. The d20 market is shrinking and the days of fat freelance rates is declining. I wouldnt be surprised to see 1 cent per word as a norm. If a company is offering you much more, you need to worry about the finanical viability of the company. Frankly a company that offers 2 cents a word and actually pays you is better than a company that offers 4 cents a word and never pays you.
Unless these are your best buddies in the world who you trust, I would be suspicious of any publisher telling an author to "name their price." Either they are trying to get you to underbid yourself, or they are novices and dont know what costs they can actually afford to pay--which might mean you wont see a dime.
Of course I could be wrong.
Clark