How do you remove a section of of a file name after underscore including the underscore using bash? [duplicate]

Question

We regularly have images that are named 1234567890_GH_ANI_EPS.eps with variables after the first underscore. I would like to write a bash script to remove the first underscore up to the file extension.

Original file name: 1234567890_GH_ANI_EPS.eps New File Name: 1234567890.eps

I was able to achieve removing the last _EPS by using the below code:

for f in "$@"
do
     mv "$f" "${f%_*}.eps"
done

And have tried the below and the file disappears:

for f in "$@"
do
     mv "$f" "${f%%_*}.eps"
done

any help would be appreciated. Thank you