OP is apparently expecting that a pathname like
is interpreted as if the last 8 digits in the filename are a date (day of month, month and year), and wants the directory name to be derived from that date.
A script for the given data might be like this:
find /Test1 -type f -mtime +2 | while IFS= read -r name
date=$(echo "$name" | sed -e 's,^/Test1/Server,,' -e 's,\.log$,,' )
[ -z "$date" ] && continue
[ "x$date" = "x$name" ] && continue
mkdir -p /Test2/"$date"
mv -f "$name" /Test2/"$date/"
although some refinement would be needed if the logfiles do not begin with the literal
Server, as well as to exclude files which do not fit the pattern.