ok, I don't plan to use the Arduino name at all, but I would credit it if requested.
It would probably be something nice to include, but if this is to be a product in which the user doesn't need to know this, it isn't necessary (just like on other products that use a ton of embedded devices, you don't see mention of the tools, etc that those use usually).
What I needed to know, was that the bootloader part were available to me.
The bootloader should be able to be implemented in your system without any legal issues, but if you are really concerned, do some more research and consult a lawyer.
I will not provide user-programmable devices, that would compete with Arduino hardware, only other, specialised hardware to do predefined tasks.
If this is going to be the case, then I wouldn't even bother with the bootloader; develop your firmware with it, then when you have it fully debugged, burn the hex binary file directly to the ATMega using an AVR ISP programmer (the same thing that is used to put a bootloader on the chip). If you need the possibility of upgrades/bug fixes (or you want to program it on the PCB, for example, if using an SMT ATMega), put in place a six pin ISP header, connected in the same manner as a standard Arduino board.
Set the proper fuses (this can tricky; I have never done this, so do some research on it) to keep any users/competitors from downloading the firmware, if you want.