I suspect the reason you see two grounds (GND and 0) is because you have both analog (GROUND) and digital (DGND) grounds in Multisim. By default, these are kept separate when you transfer to Ultiboard.
There are two ways you can connect the grounds. Which one you select depends on your particular design, but from your description, I think the first one is what you are looking for.
1. Within Multisim, select Options >> Sheet Properties. On the PCB tab, check the Check digital ground to analog ground option. You can now transfer or forward annotate to Ultiboard, and the two grounds will be connected.
2. Within Ultiboard, you can connect the different nets using a net bridge without causing DRC/Connectivity errors. Select Place >> Net Bridge, then choose and place a netbridge. If you have the ratsnest turned on, you can see that Ultiboard connects the nets through the netbridge.