In a sitcom, a man said "Go for Barny" when he pick up the phone.
Does this mean "This is Barney?"
Can I say like this when I pick up the phone?
I believe the sitcom you are referring to is "How I Met Your Mother". Barney Stinson is one of the fictional characters in the show; he is a serial womanizer who holds himself in high esteem and will do or say almost anything to get a comedic reaction from the other characters.
Stinson is seeking laughs when he answers his phone by saying "Go for Barney". I, personally, do not see the humor in answering the phone with "Go for Barney" and I wouldn't recommend that you answer your phone in this manner. A simple 'hello' will be understood by all native English speakers; the "Go for Barney" greeting will be met with bewilderment by most of the individuals who are calling you!
If you really feel the need to use your name when you answer the phone, you could say "Hello, this is Barney!" or simply use your last name by saying "Stinson".