If you want to log in every time then MottiKhan's method is correct.
You can install the second (or more) Elite program to another directory and be able to have shortcuts on your desktop for each. These are mine.
There is another way suggested by Griefed. Quoted below.
Basically, the step to setup another CMDR:
Register a Frontier account to a new email
Purchase the game.
Find your game launcher folder (right click on the shortcut to your game launcher and click Open file location)
Make a new copy of the launcher folder (Ie: "C:\Program Files (x86)\Frontier\EDLaunch - Copy" or anything you'd like)
Right click on EDLaunch.exe from the copy folder and choose copy (or alternatively, hit CTRL+C when you have EDLaunch.exe selected)
On desktop, or where you want the shortcut, right click and choose "Paste Shortcut"
Rename this new shortcut to the name of your new CMDR or however you want
You will now be able to have the 2 account authenticated without having to switch password/email every time. Each folder has it's own authentication, so no code to fetch from the trash email you registered it to.
You will have the possibility to launch each CMDR at the same time if you use the 32 bit version on one and the 64 bit on the other.
There is some other workaround to be able to launch each CMDR on the same 64 bit version, PM me if you need some details.
Update:
For those with steam install and maybe a few other exception, the full game install is located within the game launcher. If that's your situation and want to have 2 launcher without having 2 copy of the game, follow those extra step:
Select the game folder named : \elite-dangerous-64\ (64 bit version) or \FORC-FDEV-D-1010\ (32 bit version)
Cut the folder and paste it (move it) into your user\appdata which should look like this :
C:\Users"your user"\AppData\Local\Frontier_Developments\Products\FORC-FDEV-D-1010
After moving the game install there, any game launcher copy will work without having the game also situated in this copy folder.
For example, I have :
C:\Program Files (x86)\Frontier\EDLaunch
C:\Program Files (x86)\Frontier\EDLaunch - Copy
C:\Program Files (x86)\Frontier\EDLaunch - Copy (1)
C:\Program Files (x86)\Frontier\EDLaunch - Copy (2)... etc
They are all 126mb launcher install instead of full game install.
And also :
C:\Users"your user"\AppData\Local\Frontier_Developments\Products\FORC-FDEV-D-1010 (7.21gb 32bits install)
C:\Users"your user"\AppData\Local\Frontier_Developments\Products\elite-dangerous-64 (8.29gb 64bits install)