Facebook's granular privacy system helps you prevent others from seeing when you accept a friend request. Activity notifications appear on your Timeline, but you can disable these notifications. However, any friends you have in common with others appear in the friends list of other mutual friends.
What happens when you accept a friend request on Facebook?
Accepting a Friend Request means you'll add another number to your friend count, but be cautious about who you accept, as more harm than benefit can come from doing so. The next time you receive a Friend Request, take a few minutes and do a little sleuthing before clicking on that “Accept” button.
Does Facebook notify someone when you accept their friend request?
When you request a friend on Facebook, you are only notified of the status of your request if the person accepted the request. Facebook users who receive requests have the option of not taking action on your request or denying it.