Are there more descriptive ways of naming genes and gene interactions?
Many gene names are descriptive, e.g. DRD1: dopamine receptor D1, TOP2A: DNA topoisomerase 2-alpha, or PTGS1: prostaglandin G/H synthase 1. These are examples of genes that have a clearly defined main function.

The genes you listed are involved in development, and there describing the function of a gene becomes much more difficult. E.g. sonic hedgehog is involved in patterning many organs, from brain structures to teeth. How would you assign a descriptive name? 

The analogy to (programming language) functions does not work for many genes, because they were not designed to fulfill one function, but evolved to do many different functions. For genes that have many functions, we just need a unique name. The multitude of functions is catalogued elsewhere.

(Bonus descriptive gene family name: MAPKKK: MAP kinase kinase kinase)