On the Marine Corps muster rolls for July, 1944, I am interested as to what the star symbol means next to a person's name?
I have seen it next to names and enlistment dates and if you are referring to the one like in this record where they did not give it any specific meaning in the notes of the record on the same page.
The first page of that muster roll will may have a few notes, especially from the "* ", " * *", "***" notes which have very specific defined meanings in the context of that single muster roll but usually just has promotions counts and such.
Most asterisks are also defined in the footnotes found in last several pages of the muster role containing notes, detail, and general updates that came in after performing the original alphabetized muster role or with things like leave, disciplinary actions, transfers, etcetera.
I have not consistently found a procedure or abbreviation for use of a hand written star vs. a stamped star symbol but assume it was convenience and it means there is an update or further detail towards the end of the muster document like pictured below.