As per http://davdroid.bitfire.at/configuration I added two accounts for my owncloud, one for caldav and carddav each. Both show up and work as expected. But they get assigned their respective URL for displayed name, which is very long and only differs at the very end, which gets truncated on my phone.
So I would ask you to use some stripped down variation, or a user-entered name for display purposes, so those can clearly be distinguished.
(That I need to create two accounts might be also an issue, but a seperate one)