The name comes from the fact that the status message has to contain the word "dolphin," or be talking about dolphins. This way, whoever sees the messages instantly knows about its nature and can laugh at the victim.
After realizing that he/she has been "dolphined," there is a strict honor code that the victim has to follow. In particular, the message can be deleted only if none of the victim's friends has liked it yet. If the post receives at least one like it will have to be left unchanged and accessible forever, as a testimony of the victim's lameness in allowing someone else to access her Facebook.