I know close to nothing regarding bash scripting, but you might want to try this:
Code:
cd /media/DataBackup/Linux/backup/
DIR=MyData_$(date +%Y%b%d_%HH%MM)
mkdir $DIR
#this creates file MyData_current date and time
cd /home/denis/MyData/
mv *.* /media/DataBackup/Linux/backup/$DIR
Hope it helps!
LOL! While I was typing this, AlucardZero proposed the same solution (slightly different)