If your hosting company provides cPanel or another branded server admin area, you should look for the "Aliases" option in order to add a second domain.
cPanel Domain Aliases
Here's a video about how to configure Aliases in cPanel:
Configuring Addon Domains, Subdomains, and Aliases
Important: When creating the Alias, ensure that the root folder is the same as your Wordpress installation. Additionally, in some server environments "Aliases" may go by a different name and may require a different type of configuration. Other names include Domain Alias, Domain Mapping, Multi-domain, Virtual Hosting, etc. The point is to ensure that the domain uses the same root folder as your WordPress install.
You're now ready to use Domain Mapping System and start mapping domains!