If you need to store the dongle, you're probably best off with a male USB-C to female HDMI or DisplayPort adapter such as ...

9 Ports: 2x USB-C, 3x USB-A ... You can either connect direct to a USB-C monitor, or use a USB-C to either DisplayPort or HDMI adapter. The sixth USB-C port can handle 100W of PD 3.0 power ...

Another tidbit from Apple’s support document: You can connect your iPhone to an HDMI display or TV with a USB-C to HDMI adapter or cable. Adapters and cables that support HDMI 2.0 can output video ...

connecting a monitor to an iPhone required a Lightning to HDMI adapter of some sort, and was limited to 1080P video, or AirPlay to a compatible device in some cases. The addition of USB-C to both ...