Networking out of PE SA

Fortunately got a MF PE Summer Analyst offer at a firm with recognizable brand (BX, KKR, Apollo). Going to be starting this summer. However, I'm really inspired by the work that a different company outside of finance is doing and I'm going to try to pivot there for full-time recruiting.

My question is: Is it cringy to title my emails - "KKR Summer Analyst Reaching Out"? 

Should I just be sticking to my old format of "X University Student Reaching Out" or is it okay to leverage my upcoming company internship's name? 

Also, is it weird for me to be networking already before I've even started my internship?