tragen
to wear
To have clothing, jewelry, or glasses on one's body.
Heute trage ich meinen neuen Pullover.
Today I'm wearing my new sweater.

to wear / carry
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to wear
To have clothing, jewelry, or glasses on one's body.
Heute trage ich meinen neuen Pullover.
Today I'm wearing my new sweater.

In almost all of its meanings, 'tragen' is a transitive verb that requires an accusative object. The question is: Whom or what does someone/something carry, wear, support, or bear?
Sie trägt einen eleganten Hut.
She is wearing an elegant hat.
The perfect tense of 'tragen' is always formed with the auxiliary verb 'haben' (to have). This also applies when you carry something from one place to another, meaning when movement takes place.
Ich habe die schwere Kiste allein in den Keller getragen.
I carried the heavy box down to the basement by myself.
When the object of the verb is a piece of clothing, glasses, jewelry, or an accessory, 'tragen' means 'am Körper haben' (to wear / to have on one's body).
Er trägt selten einen Anzug.
He rarely wears a suit.
When it is about moving an object with the hands or body, a direction or destination is often mentioned in the sentence. This helps you recognize the meaning 'transportieren' (to transport/carry).
Die Mutter trägt ihr schlafendes Kind ins Bett.
The mother carries her sleeping child to bed.
In the meaning 'stützen' (to support), the subject is often a structural element such as a column, a beam, or a foundation. The object is then the weight or another part of the structure.
Diese Säulen tragen das gesamte Gewölbe der Kirche.
These columns support the entire vault of the church.
In the abstract meaning 'übernehmen' (to take on), 'tragen' is combined with specific nouns. Typical ones are: 'die Kosten tragen' (to bear the costs), 'die Verantwortung tragen' (to bear the responsibility), 'die Konsequenzen tragen' (to bear the consequences), or 'das Risiko tragen' (to bear the risk).
Als Projektleiter trägt er die volle Verantwortung.
As project manager, he bears full responsibility.
When it is about having a name or title, 'tragen' is used directly with the name or title as the object. This use is rather formal.
Die Brücke trägt den Namen eines berühmten Architekten.
The bridge bears the name of a famous architect.
The expression 'Früchte tragen' (to bear fruit) is based on the literal meaning used with plants. Idiomatically, it means that an effort has paid off and is leading to positive results.
Seine harte Arbeit hat endlich Früchte getragen und er wurde befördert.
His hard work finally bore fruit, and he was promoted.
to be called / to mean
'heißen' and 'tragen' can both express that someone or something has a name. 'heißen' is the normal everyday word for this, especially with people: 'Ich heiße Anna.' (My name is Anna.) 'tragen' sounds more formal or written when it is about names, titles, or designations. For example, you can say that a building, a book, or a street bears a certain name. Learners may confuse the words because both are connected with names. As a practical rule: with people in everyday language, you almost always use 'heißen'; 'tragen' is more suitable for official names or titles.

Die Schule trägt den Namen eines bekannten Schriftstellers.
The school bears the name of a well-known writer.
Die neue Kundin heißt Frau Kaya.
The new customer is called Ms. Kaya.