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.

'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.
picture / image
'das Bild' and 'der Ruf' can both mean how a person, company, or thing is seen by the public. 'der Ruf' puts more emphasis on the general opinion about someone or something, often whether it is good or bad. 'das Bild' refers more to the public impression that is created. The words are easy to confuse because both have to do with standing or reputation. 'einen guten Ruf haben' (to have a good reputation) is very common. 'ein gutes Bild abgeben' (to make a good impression) or 'das Bild einer Firma' (the image of a company) sounds more like public impact or image.

Das Restaurant hat wegen seines guten Essens einen sehr guten Ruf.
The restaurant has a very good reputation because of its good food.
Der freundliche Service verbessert das Bild der Firma in der Stadt.
The friendly service improves the company's image in the city.