EasyEDA Pro does not support setting or placing two different net names on the same wire at the same time.
Two different networks can be connected together by using a shorting character. When generating a netlist and transferring a PCB, one of the network names (naturally sorted by alphabet) will be taken as the final network name.
Entry: Top Menu - Place - Short Symbol.
As shown, VSS and DGND will be connected together, which can be viewed in the global net in the tree on the left. The final net name will be DGND.