The social engineering technique where attackers under disguise of a legitimate request attempt to gain access to is: Phishing.
Phishing can be in a form of electronic mail or website wherein attackers may present his victim a page. This website has a form that collects information from the victim. It usually appears legit as if it is from a trusted source. It is using logos of a trusted company/ individual or vendor. Once the victim has input his data, it will be automatically captured by the hacker and that's when he will get the victims credential and use it maliciously. In emails, victim will get a link or a message asking for his information. You can distinguish a phishing email because normally they contain grammar errors and they doesn't have contact details and names at all.