This is most prominently seen with people who follow astrological signs. E.g. "Well Cancers are very sentimental people, so that totally explains me/my mom/my friend". Is there a phrase or specific term for this fallacy of seeing something said about yourself by an outside source and immediately thinking "Oh, that's definitely me", even though it could apply to most people in some way? Another example could be taking a poorly designed personality test, yet still agreeing with all the results. These are most often general, blanket statements, but they don't have to be.
I'm referring to the terminology of this (usually subconscious) thought process rather than the type of person who might do it.