Scientific name for the phrase: "The first image is the image that stays" I've always heard about an effect that is entitled: The first image is the image that stays. It comes from a translation from a portuguese phrase, I don't know if it's properly translated. 

It seems that this is some kind of effect in which the way you present yourself to other person in the first meeting is the one that works as an anchor. It's a very popular saying where I live. 

My curiosity is: Does this effect really exists? I mean, has someone studied this effect?
There is another common expression: "You never get a second chance to make a first impression."

The stability of first impressions is empirically sound:


  Once formed, first impressions tend to be stable. A review of the
  literature on the accuracy and impact of first impressions on
  rater-based assessments found that raters' first impressions are
  highly correlated with later scores, but it is unclear exactly
  why. One study tested stability by asking participants to form
  impressions of people based purely on photographs. Participants' opinions
  of the people in the photographs did not significantly differ after
  interacting with that person a month later.


One possible explanation is a well-known and empirically supported cognitive bias called the "anchoring and adjustment heuristic".  It seems that people form initial impressions (anchoring), then on subsequent evaluations only make adjustments to the initial impressions, and these adjustments tend to be insufficient.  The cause of anchoring is also not well understood.

A more general explanation is "confirmation bias" (anchoring, self-fulfilling prophesy, and the halo effect are all subtypes of this bias), where people form initial impressions, and then confirm their impressions on subsequent evaluations by focusing on information that supports them, and avoiding, ignoring, forgetting, and distorting any information that does not.  This is a very empirically robust bias.