Yep, you will need the amount of members and time active before you can have your logo, I tried to ask nicely but CCP is immune to my charms and sticks to their rules
As for a corp and alliance, Ghost Festival / Naraka draws upon Buddhist traditions (is what you get with Achurans and half-Achurans in charge
). You could draw upon your own character to go with a theme, if you wish to continue with keeping that part of your RP that is.
You could also look at what activities you will be involved in: Naraka combined combat with industry in equal measures. Stillwater focusses on combat, and does exploration too, not sure if the latter is officially part of the repertoire though? Casiella is working on some project which is industry / exploration in nulsec. Pick a name suiting to what you will be doing.
One last thing you could go with is where your niche will be. All of the previously listed corps are different and fill their own niche. A successful corporation will try to fill one that is either unique or under-represented. Do I need a niche, you ask? Well, you could start very generic and go from there, but having a niche will aid in forming your vision, two things vital for corporate survival. In fact, if you were a real business and had to wrote a business plan (which you need to present to a bank to get starter funds) vision and niche are required to be written down. Mind you, that is a starting point though, if you notice along the line that things do not work out then -- just as in real life -- you can review your business plan.