I think you are confused about how it works. Also, the reason for the name is bordering on off-topic trivia.
What exactly is automatic about this repeat resending of a packet by
the server? It waits for a negative ACK, it's not automatic.
When a sender sends a segment, it starts a timer. If the timer expires before it receives an acknowledgement from the receiver, then it automatically resends the the unacknowledged segment. There is no negative acknowledgement the way you describe.
'Request'? Where is the 'request' here? An initial sending of a packet
by the sender? ACK response by the receiver?
It is an automatic repeat request based on expiration of the timer.