I am on a trip and don't have a Dash wallet installed here. I hope someone else can jump in here and help you out. In crypto wallets that I have used, you can set a password for each private key that is stored in the software.
For all of my wallets that I put in use, I print a paper copy first, then import the wallet into the software. You should be able to keep more than one private key and address combination in your software. Setting a password just prevents others from stealing your currency simply because they have physical access to your computer. If they get a printout of your private key, they can steal it, so you save that in a safe place. To create a paper copy of a wallet address, go here:
https://paper.dash.org/