Curate, connect, and discover
When Senku gets older — not old persay, maybe 30 or so — he lets his hair sit down. Brushes it back, making it look like Byakuya's did, only green at the ends instead of grey. He denies it to everyone, and of course there's no way to prove it's the same; there's no photographic evidence that Byakuya even existed.
And maybe that's why he does it. His way to let him live on in the new world as something more than a village founder, even though not a shred of dna remains.