There's an article in Wikipedia on "Null-subject" languages. It includes a section on "pro-drop" languages. So one possible answer is "pro-drop". Chinese and Japanese both drop the subject and the subject pronoun.
In Japanese, if the subject is is the speaker, it's usually indicated as the topic -- "Watashi wa" ("wa" is a topic marker) -- of the sentence and the rest of the discourse until the next instance of "wa". Until that next "wa", the listener assumes that the speaker is referring to himself/herself. Subjects take the "ga" marker. Japanese sentences are sometimes translated into English as "As for me (topic), I like fish" = "Watashi was, sakana (fish) ga suki (like) desu (it is)." The clearest translation is simply "I like fish". The structure of Japanese is quite different from English. "Fish" is the subject of the main clause in Japanese, but the object in English.
In Chinese, "I want to eat fish" is usually expressed as "Yào (want) chī (eat) yú (fish)" here in Taiwan. The complete sentence is something like "Wǒ (I) yào chī [xiǎo (small) yú] (fish)". The assumption is that the subject of the sentence is "Wǒ" if it's omitted, unless someone asks, for example, "Is Ms Chen here?" If she's not, then the answer is often "Bùzài" (Not here) instead of "Tā bùzài" (She's not here).
I've never heard the term "pro-drop" (Not a significant fact). There may be some other term as well. A linguistics professor would probably know.