For tourists, there are none. Ridesharing like Uber and Lyft is banned in Denmark. Uber was operating for two years from 2015 to 2017 before being banned. Taxis are the only alternative in Denmark (and public transport, of course). Dantaxi and Taxa 4x35 are actual taxi companies, you should be able to book a ride via their apps.
There are a few commuter-oriented "samkørsel" apps: GoMore (www.gomore.dk) and FDM Ta'Med (www.fdm.dk/ta-med), but for tourist purposes (rides to attractions etc.) you probably won't have any luck with these apps.