Here's some law regarding copyrights, trademarks and registration:
You can't copyright a name or a simple phrase.
You can copyright a written work and a software program.
You do not need to register the copyright until you wish to assert it against someone but registering enhances your claim to copyright and your damages.
You can trademark a name or a simple phrase by using it publicly in association with your product or service.
You do not need to register the trademark until you wish to assert it against someone else but registering enhances your claim to trademark and your damages.
Reserving some name on Apple's App Store Connect will not help with a trademark claim because a trademark claim requires that you use it publicly. If you reserve a name that someone else then uses publicly and they thereby establish a trademark, Apple should require that you release that name to the rightful trademark owner.