
der Ruf
reputation
The general opinion or standing that a person, organization, or thing has in public; reputation.
Das Restaurant hat einen ausgezeichneten Ruf.
The restaurant has an excellent reputation.
reputation / call
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reputation
The general opinion or standing that a person, organization, or thing has in public; reputation.
Das Restaurant hat einen ausgezeichneten Ruf.
The restaurant has an excellent reputation.

call / shout
A loud call or shout used to attract attention, call someone, or express a feeling.
Plötzlich hörten wir einen lauten Ruf aus dem Wald.
Suddenly we heard a loud shout from the forest.

professorship offer
An official offer of a professorship at a university or college.
Die Professorin hat einen Ruf an die Universität Berlin erhalten.
The professor has received an offer of a professorship at the University of Berlin.
'Der Ruf' derives directly from the verb 'rufen' (to call). All meanings are connected to this idea: reputation is what people 'rufen' (call/say) about someone, the shout is a loud call, and the 'Ruf' to a university is a formal 'Berufung' (appointment).
Sie rief um Hilfe, aber niemand hörte ihren Ruf.
She called for help, but no one heard her shout.
You can recognize the meaning from the context. Adjectives like 'gut' (good) or 'schlecht' (bad) point to reputation. Verbs like 'hören' (to hear) and adjectives like 'laut' (loud) indicate a shout. The context of 'Universität' (university) or 'Professur' (professorship) signals the job offer.
Die Firma genießt einen exzellenten Ruf.
The company enjoys an excellent reputation.
For reputation, verbs like 'haben' (to have), 'genießen' (to enjoy), 'verlieren' (to lose), or 'verteidigen' (to defend) are typical. You can also say 'einen Ruf zu verlieren haben' (to have a reputation to lose), which means that you have a good reputation and must be careful.
Durch den Skandal hat der Politiker seinen guten Ruf verloren.
Because of the scandal, the politician lost his good reputation.
In the meaning 'Schrei' (shout), 'Ruf' is often used in compound words to specify the type of call. Common examples are 'der Hilferuf' (cry for help), 'der Warnruf' (warning call), or 'der Weckruf' (wake-up call).
Die Bergsteiger sendeten einen Hilferuf aus.
The mountaineers sent out a cry for help.
This meaning is specialized language from higher education. Typical verbs are 'einen Ruf erhalten' (to receive an offer of a professorship), 'einen Ruf annehmen' (to accept an offer), or 'einen Ruf ablehnen' (to decline an offer). It always refers to the offer of a professorship.
Die Wissenschaftlerin hat den Ruf an die renommierte Universität angenommen.
The scientist accepted the offer from the renowned university.
name
Name and Ruf can both refer to a public reputation. Ein guter Name usually means an established positive reputation. Der Ruf is more neutral and can explicitly be good or bad; Ruf is therefore more suitable for a negative public opinion.

Die Firma hat wegen unzuverlässiger Arbeit einen schlechten Ruf.
The company has a bad reputation because of its unreliable work.
Die Firma hat sich durch zuverlässige Arbeit einen guten Namen gemacht.
The company has built a good name for itself through reliable work.