It's a great feature to allow naming a instance. It can be used to express the intention of the instance, such as celebrating someone's birthday.
However, I don't think it's good idea to name instance "<display name>'s instance" by default /initially because it's common to leave instance open when I leave the instance for people in the instance.
This is especially for Public instances but also for Friends plus instances.
Therefore I think the name of instance should be random by default / initially.