It should be pretty clear from the API documentation that the Locale class doesn't have any methods to install a new locale.
If you then click on the "Use" button at the top of the documentation page for Locale, that shows you everything in the standard API which uses Locale. You can check for yourself that there's nothing in this long list which installs a new Locale either.
An interesting thing you might notice in the list is that there are methods whose descriptions are like, for example, "Gets the date formatter with the given formatting style for the given locale". That implies that internally a Locale has a whole lot more baggage attached to it -- date formatters, number formatters, collators, and so on. You can't define any of that when you create a new Locale but the built-in Locales do have it.
Even the
String class has a toLowerCase(Locale) method which uses the rules of the Locale for lower-casing. You wouldn't have any way of dealing with that, either. So installing a new Locale wouldn't be all that useful any way, since you don't have a way of specifying all those Locale-dependent objects and behaviours.