LakeRat's advice is spot on. You can delete the old one .... BUT. You need to make sure you've got everything over to melovell.com first in more ways than just the files I did a double check for you and saw some gotchas.
In your wp-config.php you had this:
define( 'WPCACHEHOME', '/home/mellov/ideasinpolitics.com/wp-content/plugins/wp-super-cache/' ); //Added by WP-Cache Manager
That's the trouble with cache plugins. They don't move well Since the caching plugin wp-super-cache was removed, I removed those lines from your config file.
I also noted your SQL DB points to mysql.ideasinpolitics.com and you're using the DB for ideasinpolitics
This isn't bad, but when ideasinpolitics.com goes away, things may break.
Go to https://panel.dreamhost.com/index.cgi?tree=goodies.mysql& and add in mysql.melovell.com as an SQL database. Once that's added, you can change your wp-config.php to point to that and safely remove the hosting for ideasinpolitics.com
The DB name being ideasinpolitics is actually okay It's just the SQL server name (aka DB_HOST) that's a problem.