It's good to see more variety in corporations and cultures!
Can't help you with a corp name I'm afraid, but once you're around, feel free to contact EM for mutual blue or even +10 so you can join our fleets etc. :-)
The following are some musings I, personally, find important for a corp. You can obviously ignore any or all of it.
A new RP corp basically has to figure out both "what" they are RPing (you describe that in your post) and "how" they are RPing. This is important - it defines your "corporate culture", the thing that keeps your corp together. When recruiting, you want to recruit people who fit your corporate culture and are happy with it. If they don't, it will create unhappiness and drama in the long run. It can feel "mean", but it's usually best to simply be upfront about your corporate culture and turn down applicants when they don't fit.
For the "what", you need to figure out what is still acceptable and what is not. This is mostly an IC question. If you are anti-slavers, recruiting someone who roleplays someone who keeps slaves is likely inacceptable - even if they "roleplay that just for fun" (I've seen this argument before). Or maybe you do not really care what your members roleplay, as long as it does not affect the corp? Something to think about: Where is the line :-)
As for the "how" you RP, typical questions here that set the baseline would be: Is your corp chat IC, OOC or a mix? If it's IC, do you have a separate OOC channel? If it's OOC, do you have a separate IC channel? Do you have a public channel? Is the public channel IC, OOC or a mix? If IC or OOC, do you have a second public channel for OOC/IC respectively? And, in a slightly different angle, do you accept "I wasn't doing that IC" as a reason to "avoid" RP consequences?
One of the most difficult things for a new corp is also recruiting. You want to get a good number of people very fast - less than 10 people in corp means that even in your prime time, you will often have only 1 in corp chat. Starting from about 10 active people, that improves. On the other hand, you do not want to just recruit anyone - that, and too fast growing, is what kills corps. Finding a balance between the two is probably your biggest challenge in the beginning.
Good luck! :-)