I worked at a 10,000 person company ~15y ago. I was a lowly employee at the time; just a run of the mill Research Analyst writing code in SAS. I got on the elevator w/the CEO, said hello, and he knew exactly who I was and what I did.
Two important grounding items for me when I went into management and my career accelerated:
1. Take the worst boss I ever had (coincidentally at the same company) and make sure that I do the exact opposite of everything they did when leading others.
2. Mirror the actions of that CEO and make sure I remember every single person and what they did; it leaves a lasting impression on people.