The website name is defined once when you create the website initially. All parts configured within the system are tied to this name so it cannot be modified afterwards.
The name must start with a lower case letter, followed by lower case letters, digits, underscores or dashes. It may be only up to 32 characters long.
Among others, the name is used to configure:
system user and group
database name and username (applies only when a database is configured)
webserver vhost name
type related cronjobs
unix sockets, for example used between nginx and PHP