There are two mechanisms which could be useful here. The first one is that pin labels can be configured to display the name of the connected net instead of the component signal name. The corresponding dialog is in the component editor:
However, note that this will only display the name of the connected net, but it does not allow you to rename the net through this label.
Another way is the supply symbols approach. You might take a look at the “Supply VCC” component in the base library:
This basically works the other way around. You set a net name as the VALUE of a component. This value then gets displayed on the schematic because of the {{VALUE}} text. In addition, the “forced net” config will propagate this name to the net connected to it. So the net name is enforced by the component, not by the net (though currently renaming works only in disconnected state, this will be fixed some day).
I think both ways are not ideal for your use-case but you might still want to try it. Also keep in mind that both ways will suppress the “less than two pins in net” ERC warning as the label’s pin is considered as a real component pin.