In bash, as in ruby, the program name is given by $0. What is it in fish? I can do the following if I have to:
set PROGRAM (ps --no-header -o args -p %self | egrep -o '\S+')[2]
But I'm sure the program name must be already available somewhere. I could also set the program name in variable at the stub of each program, but that has maintenance problems.
To get the same result as your command, it is the script filename you are looking for.
This information is not stored in a variable, but you get this by querying status.
basename (status -f) # The name of the file
status -f # The full path of the file
More information: http://fishshell.com/docs/2.0/commands.html#status