Use net names to… name the net. Use ports to connect things together without naming the net. (Unless you set the project option to do so, as mentioned already, which of course I would not do in this instance.)
(Ports are like segments of wire that have simply been hidden from view.)
Indeed, your design may be a candidate for multichannel design, in which case you can adjust the naming pattern to a point.
P.S. You can easily convert net labels to ports or vice versa using the Smart Paste feature. Select the net labels, cut them, then Smart Paste > as Ports, with the order set to stay the same.