It's less that other letters are reserved, and more that there are only eight general-purpose registers, and four of them already have special meanings.

A is the accumulator, F is flags, and as the sibling comment mentioned, H and L represent the high and low bytes of HL, which is the only 16-bit register you can use for indirect memory access in most instructions. It's also used in some control-flow instructions.

That leaves four remaining registers, which just so happen to fit perfectly into the remaining space: B, C, D, and E. (They can also be accessed as BC and DE with 16-bit instructions.)

The H and L registers are special in that they can be used for indirect addressing: some opcodes will combine H (high) and L (low) into a 16-bit number, interpret that as an address and read from that memory location.