An easy way of making your Pi that little bit more secure is to remove the default user, Pi.  So when setting up a new Pi installation this is one of the first things I do which is very simple.

SSH into your Pi as usual:

ssh pi@192.168.0.2

Switch to the root user:

sudo -i

Create a new user:

adduser puk

Will result in the below, add a decent password when asked and then repeat it:

Adding user `puk' ...
Adding new group `puk' (1001) ...
Adding new user `puk' (1001) with group `puk' ...
Creating home directory `/home/puk' ...
Copying files from `/etc/skel' ...
Enter new UNIX password: <REDACTED>
Retype new UNIX password: <REDACTED>
passwd: password updated successfully
Changing the user information for puk
Enter the new value, or press ENTER for the default
	Full Name []: Puk
	Room Number []: 
	Work Phone []: 
	Home Phone []: 
	Other []: 

Is the information correct? [Y/n] Y

Add the new user to the sudo group:

adduser puk sudo

Adding user `puk' to group `sudo' ...
Adding user puk to group sudo
Done.

Quit the Pi by typing exit a couple of times, first to log out as root then to leave SSH. Log back into the PI with SSH using your new username/password:

ssh puk@192.168.0.2

Now to delete the old Pi user:

sudo deluser pi

Will give you an output, add the user Pi’s password when asked:

We trust you have received the usual lecture from the local System
Administrator. It usually boils down to these three things:

    #1) Respect the privacy of others.
    #2) Think before you type.
    #3) With great power comes great responsibility.

[sudo] password for puk: 
Removing user `pi' ...
Warning: group `pi' has no more members.
Done.

Finally change the default password of the root account, use a new pass when asked:

sudo passwd root

Enter new UNIX password: 
Retype new UNIX password: 
passwd: password updated successfully

Job done!