Find all files with the extension .pdf, cut the path of the file and store the second part of the path in a variable, then move the file to a new location with the name of the current date and time followed by the variable.
find -type f -name '*.pdf' | cut -d/ -f2 | xargs -I {} mv "{}" "./$(date +'%Y-%m-%d-%H-%M-%S')-{}"