I am labeled as a "Merciful Thug". Is there anyway I can get back to neutral. I can still talk to NCR and go to NCR bases so they are not hostile.
I don't know how it dropped I must have killed somebody in the NCR without realizing it. But is there any efficient ways to raise it?

if you do quests for them, you should eventually go back up to neutral. what is their stance to you?

Or if you go far enough in the campaign they will send someone to you saying ambassador Crocker wants you to get the Boomers to help NCR and then make you neutral to them after talking to you

The most fame raising quests are the ones at Camp McCarren. Talk to Colonel Hsu about all of those quests, then in the food area there's Private Morales she has one, and then there's Major Diharti out in the yard who has one that is worth 3 fames up.