The following simple Bash script adds a year-month-date string to the file name, which makes its time stamp more apparent in a file explorer. Also note that in the grep command, the Perl-compatible regular expression is adopted.

#!/bin/bash

modification_date=$(ls -l "$1" --full-time | grep -P "\d{4}-\d{2}-\d{2}" -o)
mv "$1" "$modification_date-$1"