Use a loop and copy each file individually. To compute the new name you can use sed or bash's built-in parameter expansion.
Both of the following scripts assume that you don't have any directories starting with Pep.
The following script copies each file starting with Pep in the working directory. The new names will have the first Pep removed. The -n option avoids accidentally overwriting of files.
for f in Pep*; done
cp -n "$f" "${f#Pep}"
done
To include sub-directories you can use bash's globstar built-in.
shopt -s globstar nullglob
for f in ./path/to/main/dir/**/Pep*; do
cp -n "$f" "${f//\/Pep/}"
done
Always start the path with ./ or / so that the script can distinguish between Pep at the start of a filename and Pep inside a filename, for instance Pep do not replace Pep in the middle.txt.
And here's an equivalent script that should work in every POSIX shell, including ancient bash versions as the one on Macs.
find path/to/your/main/directory -type f -name Pep\* -exec sh -c \
'echo cp -n "$0" "$(printf %s "$0" | sed -E "s:(.*/)Pep:\1:")"' {} \;