eingetragen
registered
Officially recorded in a register, list, or official directory and therefore legally recognized or protected.
Unser Sportverein ist ein eingetragener Verein (e.V.).
Our sports club is a registered association (e.V.).

registered / broken in
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registered
Officially recorded in a register, list, or official directory and therefore legally recognized or protected.
Unser Sportverein ist ein eingetragener Verein (e.V.).
Our sports club is a registered association (e.V.).

'Eingetragen' is the past participle of the separable verb 'eintragen' (to enter/register). Here it is used like an adjective to describe a noun that has been 'eingetragen' (entered/registered) into something.
Die eingetragene Marke ist rechtlich geschützt.
The registered trademark is legally protected.
You can recognize the meaning from the context. If it is about legal or official topics (association, trademark, company), official registration is meant. If it is about clothing or shoes, it refers to the comfortable, worn-in form.
Der Name unserer Firma ist als Marke eingetragen.
The name of our company is registered as a trademark.
In a legal context, you will often find the combinations 'eingetragener Verein' (registered association, often abbreviated as 'e. V.'), 'eingetragene Marke' (registered trademark), or 'eingetragene Lebenspartnerschaft' (registered civil partnership).
Die Abkürzung „e. V.“ steht für „eingetragener Verein“.
The abbreviation 'e. V.' stands for 'eingetragener Verein' (registered association).
When clothing or shoes are 'eingetragen' (broken in), it has a positive meaning. It means they are no longer stiff, but have become soft and very comfortable through long wear.
Meine eingetragenen Stiefel sind perfekt für lange Wanderungen.
My broken-in boots are perfect for long hikes.
protected
'geschützt' and 'eingetragen' can both have to do with legal security, especially with trademarks, names, or rights. 'eingetragen' means that something is officially listed in a register. As a result, it may be legally recognized or protected. 'geschützt' describes the result: others are not allowed to simply copy or use it. The words can be confused because a registered name is often protected. But not every use of 'geschützt' explains where or how something was officially registered.

Die Marke ist seit Montag im Register eingetragen.
The trademark has been registered in the register since Monday.
Der Name der Firma ist geschützt und darf nicht einfach kopiert werden.
The company's name is protected and may not simply be copied.