The design of finite alphabets is an application-oriented work for communication systems. In this paper, we investigate this for photon-counting based broadcast underwater visible light communication (UVLC) systems. For the demand of energy-efficiency and unique identification, our designs are conducted under the constraints of Hellinger distance criterion and uniquely decomposable constellation group (UDCG) theory and generate two kinds of multilayer modulation (MLM) constellation for different overall bit rate cases: Integer and non-integer. Correspondingly, for these two kinds of designs, we provide fast square root (FSR) receivers whose complexity are lower than that of the currently available maximum likelihood (ML) receiver. Finally, we investigate the achievable rates of downlink Poisson non-orthogonal multiple access (NOMA) and our proposed MLMs. The benefits of these designs revealed by demonstrations or simulations include that: 1) For the considered system, the proposed MLMs have a considerable performance advantage over TDMA and admit fast square root receiver at the cost of a moderate performance penalty compared with the ML receiver; 2) Compared with the Poisson NOMA, the proposed MLMs do not require successive interference cancellation (SIC) and their achievable rates exceed the achievable rate region of Poisson NOMA in high power regimes.