To determine the correct order in each set, we need to identify which names follow a logical sequence or pattern. Here's the analysis for each:
A. Hansen, Johnsen, Petersen, Helen - This seems to contain surnames of Scandinavian origin (Hansen, Johnsen, Petersen), while "Helen" is a first name, which breaks the pattern of surnames.
B. Finley, Finely, Finner, Feinmeister - "Finley" and "Finely" can be variants of the same name, while "Finner" and "Feinmeister" don't clearly follow a recognizable pattern or relation.
C. Buckley, Bucky, Bucled, Bernstein - "Buckley" is a surname, "Bucky" can be a nickname derived from it. "Bucled" does not seem to relate closely, nor does "Bernstein," which is a different surname.
D. Andersen, Anderson, Andyson, Anglerton - Both "Andersen" and "Anderson" are variants of the same surname, "Andyson" would suggest a continuation or nickname, and "Anglerton" seems out of place.
Hence, the best option that maintains a somewhat coherent order is D - Andersen, Anderson, Andyson, Anglerton - as it appears to focus on variations or derivations stemming from "Andersen" or "Anderson".