Name of cognitive bias when you diminish one's competency based on someone else's for the same function? Let's say you have a REALLY good manager, and he leaves. So you tend to underestimate/judge the next manager's competencies because the previous one was really good.

How you call the cognitive bias related to that ?
The broad topic is norm theory. Kahnemann &amp; Miller (1986) give a nice overview of the topic. The specific effect is a contrast effect.

Higgins &amp; Lurie (1983) have an experiment which matches the situation nicely. In their experiment, subjects read a series of short stories describing the sentences handed out by various judges for similar crimes. Some judges were harsher or more lenient than others. As you might expect, a specific sentence (e.g. Judge Wilson sentenced the guilty person to 3 years of prison) was judged as being more harsh if the other judges tended to give shorter sentences, and more lenient if the other judges tended to give harsher sentences. 

Their result also suggests that your memory of the first manager's competency (the really good manager) will be affected by the exposure to the new manager. They brought the subjects back to the lab a few days after reading the original stories. When subjects came back, they were given a new set of sentencing decisions to read. Then they were asked to recall how long the sentence was of a specific judge (e.g. Judge Wilson) from the first session. The memory for the original sentence was skewed by the new stories that they read. If the new stories all tended to be lenient, then subjects underestimated Judge Wilson's original sentence. If the new stories were all harsh, then subjects overestimated Judge Wilson's original sentence. They call this a change-of-standard effect.