Can you own several player names?

I really dont want anybody to steal my name in mc but i want to change my name, If you change your name do you still own your name? Lets say if your name is chloe, then you change it to chloea. Can another player change their name to chloe even though you used to own that name?

Here is the Mojang page on the subject:

If you've changed your username already, you'll need to wait 30 days to be able to make another change. 

If you change your username, your old name is held for 37 days. This gives you an extra week to change back if you've made a mistake or changed your mind before your previous username becomes available to anyone else. 

So yes, after 37 days, someone else can have your old user name.