cPanel & WHM contains a feature that does what you are asking. The feature is called ‘Proxy Sub Domains’. Here’s how to enable it:

1. Login to WHM with root level access
2. Click Tweak Settings
3. Go to the Domains section
4. Enable Proxy Sub Domains

More information is available in the documentation: https://documentation.cpanel.net/display/1152Docs/Tweak+Settings+-+Domains#TweakSettings-Domains-Proxysubdomains

Note: since cPanel & WHM installs the Apache web server, you already have everything you need to access the cPanel & WHM service via ports 80 and 443.

To the best of my knowledge, the cPanel/WHM daemon does not restrict access to a particular name but instead respond to any name pointed at the droplet. So, handling the name is juts a matter of pointing the name to your droplet.

Translating port 2087 to port 80 or 443 (what is used if no port is specified) would require something like a second server running nginx as a reverse proxy since port 80 and 443 on your droplet are already being used by your public web services.