Yes, this can be done in Calc
First,assign a unique number to the names, i did put those number in column B, so i get:
Names Seqeuence
Jack 3
Jill 2
Sam 1
Susan 4
Bill 6
Joe 5
Then, i have this foruma in D2:
=INDIRECT("A"&TEXT(B2+1;"0"))
which i copy from B2 to B3..B7
i get:
Names Seqeuence
Jack 3 Sam
Jill 2 Jill
Sam 1 Jack
Susan 4 Susan
Bill 6 Joe
Joe 5 Bill
Last bit:
In E5: =D2&","&D5
Copy this from D2 to D3..D4
Result:
Names Seqeuence
Jack 3 Sam Sam,Susan
Jill 2 Jill Jill,Joe
Sam 1 Jack Jack,Bill
Susan 4 Susan
Bill 6 Joe
Joe 5 Bill
Next time, the sequence is different, resulting in:
Names Seqeuence
Jack 6 Joe Joe,Jill
Jill 3 Sam Sam,Bill
Sam 1 Jack Jack,Susan
Susan 2 Jill
Bill 5 Bill
Joe 4 Susan