Economic Confirmation Biases
Confirmation bias is somewhat different to the behavior you are describing. This expression describes the attitude of a researcher who interprets ambiguous data as confirming his initial hypothesis. For instance, researchers who believe that death penalty has a deterrent effect on crime would interpret any additional dataset as confirming this theory, whereas researchers who believe the opposite would interpret the same evidence as indicating that the effect is null.

The behavior that you describe might be called "post hoc analysis" or "post hoc theorizing". Scientific standards in experimental economics have been  improving recently to mitigate this bias (among other mistakes/misbehavior). For instance, many researchers who do randomized controlled trials in development economics now pre-register their analysis plan (and even sometimes a theory with its predictions) before collecting the data: by doing so, they commit to a list of statistical tests that they will run, which prevents them from changing their theory/hypotheses (and even the question of interest) after looking at the data. Of course, as @denesp mentions, this cannot generally be done with observational data, except maybe in situations where the researchers need to go through an approval procedure to get access to the data, in which case a pre-registration of the analysis plan might be imposed as part of the application.