On Instagram, you can remove a comment you made on any photo or a comment someone else made on a photo you posted. If someone mentions your username in his comment, you can't remove it -- you can ask the person to remove it and you can block him. If you're tagged in somebody's public photo or you follow that person, you'll be notified, and you can prevent the photo from displaying on your profile or untag yourself from the picture. However, if someone you don't follow tags you in a photo and shares it privately, you won't be notified and you can't untag yourself.
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Comments
Step
Open the Instagram app. Press "News" to open the News tab to review notifications that someone has commented on one of your pictures; that your username has been mentioned in a comment on someone else's photo; or that you've been tagged in a photo.
Step
Press and hold a user's name and select "Go to user." Send the user a message and ask him to remove your username from his comment on a photo. Press the "Menu" option and choose "Block" to prevent the user from mentioning your username in a comment or tagging you in a photo in the future.
Step
Press the "Comment" button below a photo, swipe left or right on the comment you want to delete, and then choose "Delete" to delete a comment you've posted or a comment someone else has posted on one of your photos.
Tags
Step
Navigate to the News tab and look for notifications that you've been tagged in a photo. Press the photo to load it, tap your name and select "Hide from My Profile" to prevent the photo from showing up in your profile, which is the default setting.
Step
Go to your profile, press the "Photos of You" button, press the "Menu" button, and then choose "Add Manually" to require your approval of photos before they display on your profile.
Step
Display a photo you've been tagged in and press "... | Photo Options | More Options | Remove Me From Photo" to untag yourself.