If you're using Bash, you don't even have to use grep:
files="*.jpg"
regex="[0-9]+_([a-z]+)_[0-9a-z]*"
for f in $files
do
[[ $f =~ $regex ]]
name="${BASH_REMATCH[1]}"
echo "${name}.jpg" # concatenate strings
name="${name}.jpg" # same thing stored in a variable
done
Edit: It's better to put the regex in a variable. Some patterns won't work if included literally.
This uses =~ which is Bash's regex match operator. The results of the match are saved to an array called $BASH_REMATCH. The first capture group is stored in index 1, the second (if any) in index 2, etc. Index zero is the full match.
You should be aware that without anchors, this regex (and the one using grep) will match any of the following examples and more, which may not be what you're looking for:
123_abc_d4e5
xyz123_abc_d4e5
123_abc_d4e5.xyz
xyz123_abc_d4e5.xyz
To eliminate the second and fourth examples, make your regex like this:
^[0-9]+_([a-z]+)_[0-9a-z]*
which says the string must start with one or more digits. The carat represents the beginning of the string. If you add a dollar sign at the end of the regex, like this:
^[0-9]+_([a-z]+)_[0-9a-z]*$
then the third example will also be eliminated since the dot is not among the characters in the regex and the dollar sign represents the end of the string. Note that the fourth example fails this match as well.