Nextcloud is simply software that runs on something. You might use DNS to find the something that your Nextcloud runs on ... or not. A domain can cost as little as say £10/year (no details given - loose costing provided!) but you say you don't want one.

You could do some weird stuff involving something like this: Your clients update a database on the server with their current IP address(es) and the server reciprocates in kind regularly.

For an internets conversation, both sides need to know IP address, protocol, and optionally port; for both ends. For example, a webby conversation might involve:

My end: 192.168.100.20/24, tcp port 2399 -> NAT -> 33.22.4.66, tcp port 2245 Remote web server: 99.22.33.44/37, tcp port 443

Now, provided both sides are warned off about changes to addresses and port numbers on a regular basis, then comms will still work.

Say, your home external IP address changes, then your browser writes that new address to the remote server and comms continue. Provided one end knows all the details of the other end at any point in time and can communicate local changes then we are good.

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Maybe not. Lookup: Dynamic DNS.