A high/low profile
Definition 1 of 2
Pro Tip 1/3Media Attention
Relates to how much media coverage a person or organization receives. 
Since the award, the scientist has had a high profile in the media.
Pro Tip 2/3Privacy Strategy
Some people deliberately maintain a low profile to protect their privacy. 
Celebrities often use hats and sunglasses to keep a low profile.
Pro Tip 3/3Avoiding Controversy
A low profile can mean avoiding taking strong public stances to stay out of debates. 
The politician kept a low profile during the heated debate.