Here is something i put together with some information i found here.
#!/bin/bash
searchterm="<ProjectName>"
replaceterm="New Project"
srcsvnrepo="file:///svnrepoaddress"
destsvnrepo="file:///data/newrepo"
dumpfile="/home/<user>/repo.dump"
tmpfolder="/home/<user>/tmp_repo"
svnadmin dump $srcsvnrepo > $dumpfile
svnadmin create --fs-type fsfs $destsvnrepo
svnadmin load $destsvnrepo < $dumpfile
svn co $destsvnrepo $tmpfolder
for file in $(grep -l -R $searchterm $tmpfolder)
do
sed -e "s/$searchterm/$replaceterm/ig" $file > /tmp/tempfile.tmp
mv /tmp/tempfile.tmp $file
echo "Modified: " $file
done
svn ci $tmpfolder --message "Initial Check-In"
Basically this will dump a backup of the specified source svn repo to a file, create a new repo, load the backup into it, check out the files, get a list of files that contain the string to search for, perform a regex on each of those files storing the new version in a temp location and then moving the temp file back to the original location, and finally checking the changes back into the new repo.
I haven't fully tested this so some minor tweaking may be necessary, but the basic steps should be correct. Please let me know if i've made some gross miscalculation and this totally does not work.