But both databases send invoices and links. How do I set it up?

By reading the documentation yourself: www.odoo.com/documentation

I've read that several times. But, I don't understand how to set it up in a way that myco.company.com uses a DB and otherco.company.com uses another DB

Check this: https://www.odoo.com/forum/help-1/question/odoo-8-0-apache2-how-to-configure-a-proxy-from-an-url-to-a-specific-database-in-a-multi-database-setup-110545#answer-110604

I got it!

The DB name must match the domain or subdomain name, depending on your setup of the db-filter. So, if using %d, myco.company.com must use a db named myco and otherco.company.com must use a db named otherco.

Thank you very much Ermin. I really appreciate all your help.

Then please show your appreciation by upvoting and ticking the answered mark :-)

I tried, but it says I don't have karma enough to transform a comment into an answer

Well, I marked your first answer. If any body reach it, would need to read all the comments. ;)

You don't need no karma, because you do not have to convert anything, you already ticked as answer I see, and upvoting is done by clicking the small triangle above the 0 right beside it.

I did amend my answer :-)

Anyway, for others it would also be helpful to upvote the linked answer, as it is more generic concerning the use of dbfilter.

Done!!

Thanks for taking the time to explain upvote ;)

Thanks :-)