ill fame(n = noun.state) notoriety - the state of being known for some unfavorable act or quality;
is a kind of infamy
has particulars: reputation

fame, hall of fame, house of ill repute, ill, ill at ease, ill health, ill humor, ill humour, ill luck, ill nature, ill repute, ill service, ill temper, ill turn, ill will, mentally ill, national baseball hall of fame