If you want to ask the user for a second name, just ask the user for a second name:
#! /bin/bash
echo "Enter name of dir":
read folder1
echo "Enter name of sub-dir":
read folder2
mkdir -p -- "$folder1/$folder2"
touch docu.dat
chmod 755 docu.dat
Although I suspect that you want to create docu.dat inside the directory you just made, in which case you'd want this:
#! /bin/bash
echo "Enter name of dir":
read folder1
echo "Enter name of sub-dir":
read folder2
mkdir -p -- "$folder1/$folder2"
touch -- "$folder1/$folder2"/docu.dat
chmod 755 -- "$folder1/$folder2"/docu.dat
However, as a general rule, try to avoid prompting the user for input. That makes the script very hard to automate, very hard to re-run, it is easy for a user to enter a wrong value etc. Instead, take the directory names as arguments:
#! /bin/bash
dirName="$1/$2";
mkdir -p -- "$dirName"
touch -- "$dirName"/docu.dat
chmod 755 -- "$dirName"/docu.dat
And then run the script like this:
./script.sh "dir1" "dir2"
The -- are there so that your script can also handle directory names starting with a -. See What does "--" (double-dash) mean?.