I'm looking for research I've read about a well known effect that happens when participants complete a survey, where they do not answer what they think is right, but what they think the researchers are expecting from them. It can be a survey but it can also be something else...
This is called "demand characteristics":
... an experimental artifact where participants form an interpretation of the experiment's purpose and unconsciously change their behavior to fit that interpretation.
An example is:
The good-participant role in which the participant attempts to discern the experimenter's hypotheses and to confirm them. The participant does not want to "ruin" the experiment.
Demand characteristics are a type of response bias:
... a general term for a wide range of cognitive biases that influence the responses of participants away from an accurate or truthful response. These biases are most prevalent in the types of studies and research that involve participant self-report, such as structured interviews or surveys.
Another related type of response bias is the "social desirability bias":
... the tendency of survey respondents to answer questions in a manner that will be viewed favorably by others.