Learn Portuguese (Portugal): Este casaco pertence à Rita.

The word à is a contraction of the preposition a (to) and the feminine definite article a (the). The verb pertencer (to belong) requires the preposition a. Because Rita is a woman's name, it takes the feminine article a. When you combine a plus a, you get à with a grave accent to show the contraction.

Why do we add an article before the name to make it à Rita?

In European Portuguese, it is standard to use a definite article (o or a) before a person's first name in everyday speech. Therefore, we use the feminine article a before Rita. While in English we just say 'belongs to Rita', the Portuguese literally translates as 'belongs to the Rita'.

Could I use esse instead of este for 'this coat'?

Not if you want to say 'this'. Este means 'this' and is used for an object physically close to the speaker, like a coat you are currently holding or wearing. Esse means 'that' and is used for an object close to the person you are talking to.

How is the verb pertencer conjugated here?