Some citation styles require to replace any subsequent occurences of the same author/bookauthor/editor by idem/eadem, their abbreviations id./ead., or some other term or symbol like a dash.

a) It may be that you need such replacements within the bibliography, e.g.

 Doe, Johnson & Williams. 2001.
 --- & Smith. 2002.
 Doe, Stevens & Miller. 2003.
 ---, --- & ---. 2004.

This is possible and just depends on the citation style you use. (If you want to use it in your own citation style, see subsequent-author-subsitute rules in CSL.)

b) It may be that you need such replacements within one reference, for example for a work in an anthology (collected or selected work), e.g.

 DOE, JOHN (1998): Article. In: IDEM (ed).: Book.

This is currently not possible, but as a workaround you can enter here in Zotero “IDEM” as the book author or editor, which will give you the desired result.

c) It may also be that you need such replacements for subsequent citations of the same author but different books, e.g.

 V. HUGO, Les Misérables, Livre de poche, 2002, p. 127.
 ID., La Légende des siècles, Hatier, 1998, p. 45.

This is currently not possible, but as a workaround you can suppress the author here and add “ID., ” manually.

Main thread for this issue: https://forums.zotero.org/discussion/4785/check-for-identical-authoreditor/