For negative notoriety:
* Obscurity: This means being unknown or unimportant.
* Anonymity: This means being nameless or unidentified.
* Unremarkableness: This means being ordinary and not standing out.
* Insignificance: This means being unimportant or having little impact.
For positive notoriety:
* Respect: This means being admired and held in high regard.
* Esteem: This means being highly valued or respected.
* Fame: This means being widely known and admired for positive reasons.
Other possibilities:
* Privacy: This is the state of being free from unwanted attention.
* Quietness: This means being calm and peaceful, without any attention-grabbing events.
The best opposite word for "notoriety" will depend on the specific context and the nuance you want to convey.