Can shell variable name include a hyphen or dash (-)?

I've never met a Bourne-style shell that allowed - in a variable name. Only ASCII letters (of either case), _ and digits are supported, and the first character must not be a digit.

If you have a program that requires an environment variable that doesn't match the shell restrictions, launch it with the env program.

env 'strange-name=some value' myprogram

Note that some shells (e.g. modern dash, mksh, zsh) remove variables whose name they don't like from the environment. (Shellshock has caused people to be more cautious about environment variable names, so restrictions are likely to become tighter over time, not more permissive.) So if you need to pass a variable whose name contains special character to a program, pass it directly, without a shell in between (env 'strange-name=some value' sh -c'…; myprogram' may or may not work).

That's not possible in Bash.

From the Definitions section in the manual page of bash:

name A word consisting only of alphanumeric characters and underscores, and beginning with an alphabetic character or an underscore. Also referred to as an identifier.

From the Parameters section in the manual page of bash:

A parameter is an entity that stores values. It can be a name, a number, or one of the special characters listed below under Special Parameters. A variable is a parameter denoted by a name.

You can access a hyphenated variable using an indirect reference.

$ env 'my-hyphenated-variable=hello' /bin/bash
$ name='my-hyphenated-variable'
$ echo ${!name}
hello