Apple - Change Appstore user from MacBook?

You will need to go to Store->Sign Out, then sign in with your own account.

After that, delete the software that is asking for the old account password, and reinstall it under your account. If the software is not free, you will need to buy the software again. You do not have a license to use the software, unfortunately.

In your case, there’s only keynote needing an update so you know keynote had that account tied to it.

To switch Appstore user you can go to 'Featured' tab -- there link named as "Welcome " is clickable and open the window with the button "Log out".