fame or notoriety?
In contemporary English notoriety is correctly used to mean only "the condition of being well-known for something disgraceful or otherwise undesirable," as in a mayor whose notoriety stems from election fraud. A word with a similar meaning is infamy. Fame on the other hand is simply "the condition of being very well known," as in a governor whose fame [not notoriety] stems from his heroic service in the Korean War. The same distinction holds with the adjectives notorious (and infamous) and famous ("widely known").
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