What is meant by "Stand-Alone Instance of SQL Server" I am cloning a server to perform an in-place upgrade and I will have to change the name of that server - which has a SQL Server with just one instance (default instance) installed on it. 

I am reading this article and it keeps referring to "stand alone" instance" of SQL Server. What is meant by stand alone here?
Stand Alone:


  Operating, functioning, or existing without additions or assistance; independent; able to be separate or separated.


And that's precisely what is referring to on that article, to a self-sustained SQL Server instance, not participating (as Aaron commented) on a Failover Cluster or a WSFC. That's why the article refers to some scenarios where renaming there computer is directly forbidden or it could wreak havoc as it's not a "stand alone" but part or some other process.