How to find bash commands?

compgen -c | grep -i "user"

compgen [option] [word]

Generate possible completion matches for word according to the options, which may be any option accepted by the complete builtin with the exception of -p and -r, and write the matches to the standard output.

The matches will be generated in the same way as if the programmable completion code had generated them directly from a completion specification with the same flags. If word is specified, only those completions matching word will be displayed.

...

-A action The action may be one of the following to generate a list of possible completions:

alias Alias names. May also be specified as -a.

arrayvar Array variable names.

binding Readline key binding names (see Bindable Readline Commands).

builtin Names of shell builtin commands. May also be specified as -b.

command Command names. May also be specified as -c.

directory Directory names. May also be specified as -d.

disabled Names of disabled shell builtins.

enabled Names of enabled shell builtins.

export Names of exported shell variables. May also be specified as -e.

file File names. May also be specified as -f.

function Names of shell functions.

group Group names. May also be specified as -g.

helptopic Help topics as accepted by the help builtin (see Bash Builtins).

hostname Hostnames, as taken from the file specified by the HOSTFILE shell variable (see Bash Variables).

job Job names, if job control is active. May also be specified as -j.

keyword Shell reserved words. May also be specified as -k.

running Names of running jobs, if job control is active.

service Service names. May also be specified as -s.

setopt Valid arguments for the -o option to the set builtin (see The Set Builtin).

shopt Shell option names as accepted by the shopt builtin (see Bash Builtins).

signal Signal names.

stopped Names of stopped jobs, if job control is active.

user User names. May also be specified as -u.

variable Names of all shell variables. May also be specified as -v.

You may want to check for spaces in some path and improve it with more powerful regex, but this does the trick:

#!/bin/sh

if [ $# -ne 1 ]; then
   echo "Usage: $0 pattern"
    exit 1
fi

for x in `echo "${PATH}" | sed 's/:/ /g'`; do
    for y in $x/*; do
        if [ -x "$y" ]; then
            if [ `echo "$y" | grep $1 | wc -l` -ne 0 ]; then
                echo "$y"
            fi
        fi
    done
done

If you want to find all commands in a directory, on Linux you can use:

find /bin -type f -perm -o+x  -name '*z*'

In this example, it will list all executables (programs) on /bin directory that had a z in their name. If you want to search in multiple directories, you can write a script and call the find in a loop, one time for each directory.

You can combine this with the previous answer to search in all directories on your path:

find $(echo $PATH | tr ':' ' ') -type f -perm -o=x  -name '*z*'