Should I change 'name' in composer.json, from 'laravel/laravel' to the name of my own project...?

A tiny detail, perhaps, but I'm trying to improve my grasp of composer and packages, and clarity of working.

A new laravel install is a copy of laravel/laravel, i.e., the application skeleton. In composer.json of that package, 'name' is laravel/laravel, and 'description' is 'The Laravel Framework'.

Since, in a new app, this skeleton is code I am about to modify into my own app, should I alter the values of 'name' and 'description' as above, and effectively make this into a new composer package? (even if I'm not necessarily planning to publish it as one).

This is obviously to benefit from the license which allows this to be done.

The dependencies are going to be the same as that of laravel/laravel, with my additions.

But the name of the package will no longer be laravel/laravel, - it can now be my own name.

This comes about because laravel/laravel is not a dependency of anything, it's just what you start with and modify for your own purposes.

Have I misunderstood or missed anything?