Immortality is an interesting thought experiment. Yes, looking young while being shockingly old is a fun thing to suprise people with, but the concept of time itself would be so terrible that everything would be a blur. Your friend would have to correct you on what happened when.
"That happened in the 60s,"
Really? What century?
"1960's."
Was that during speakeasies?
"No, that was during the 1920's. The 60's had hippies and Woodstock."
Oh, yeah. Everything's been a blur since everyone got a car.
They'd also probably forget EVERYONE'S name because the immortal has been around for so long. So it'll feel like you're doing with your great grandparents all the time.
Henry?
"No, I'm Steve."
Oh. You remind me of Henry.