You can use the bash(1) built-in compgen
compgen -c
will list all the commands you could run.compgen -a
will list all the aliases you could run.compgen -b
will list all the built-ins you could run.compgen -k
will list all the keywords you could run.compgen -A function
will list all the functions you could run.compgen -A function -abck
will list all the above in one go.
Check the man page for other completions you can generate.
To directly answer your question:
compgen -ac | grep searchstr
should do what you want.