According to Mills EE,
2.70 NAMES, MAIDEN
The discipline of genealogy uses parentheses to distinguish the maiden
names of married females. In the case of females who have a succession
of husbands, the parentheses should not be placed around the other
surnames she acquired by marriage—e.g.,
Hannah (Baskel) Phelps Phelps Hill
Hannah (Baskel) (Phelps) (Phelps) Hill
2.72 Quotation Marks
The genealogical convention for writing nicknames is to place them in
quotation marks immediately after the formal name for which they
substitute—e.g., Margaret "Peg" Monroe.
3.39 School Records, Heirloom Copies
As discussed in 2.72 and demonstrated above in note 1, nicknames
are conventionally placed in double quotation marks immediately after
the given name. They should not be placed in parentheses, because
that convention is used for the maiden surname of females, as discussed
in 3.20 and illustrated further at 3.37 and 3.40.
In the case of Mary Adams, formerly Thompson, previously Jones, née Smith, if I interpret the ambiguity correctly, would be listed as
Mary (Smith) Jones Thompson Adams.
Of course, the Name Source Field Type cannot handle this situation in Source Templates. Breaking the name into three fields allows the appropriate arrangement for Source Citation.
<[GivenName]>< ([MaidenName])>< [LastNames]>
Mary (Smith) Jones Thompson Adams
< [LastNames], ><[GivenName]>< ([MaidenName])>
Jones Thompson Adams, Mary (Smith)
While I can't find a specific reference for it, I am doubtful that this would be an appropriate bibliographic entry with all three married names. I believe for Source Citation purposes that Mary (Smith) Adams and Adams, Mary (Smith) would be appropriate, but hey...