Empathy, perhaps? Empathy means "the intellectual identification with or vicarious experiencing of the feelings, thoughts, or attitudes of another." How more personal can you get?
Rapport, which is a noun that means "a relationship, especially one of mutual trust or emotional affinity", may also be what you're looking for.
Noun - Rapport : "His success came from having a good rapport with his customers."
Defination according to Wikipedia: Rapport is one of the most important features or characteristics of unconscious human interaction. It is commonality of perspective: being "in sync" with, or being "on the same wavelength" as the person with whom you are talking.
Can you clarify what you are asking? Do you mean specific vocabulary for meeting people and making friends?
e..g.
Nice to meet you.
You look lovely today.
Thank you for helping me out.
Can I help you?