What to call the cells of memory in a computer or a microcontroller?
In my mind, a register is a storage location that is within the CPU, or directly addressable by the CPU - things like the Accumulator, index registers, and similar things. I would not say that EPROM, FLASH and RAM have registers.

If you look at the assembly-language instruction set for a microprocessor or microcontroller, you will see that some instructions deal with registers, while others deal with RAM, EPROM or FLASH memory access, so the processor sees a register as something different than a memory location.