Sometimes, you will see citations like “(J. Smith 2000, J. R. Smith 2001)”, even though your citation style normally only shows the author's last name (“Doe 2004”). In these cases, Zotero is trying to disambiguate different authors. This can also occur when a certain author is inconsistently named in your Zotero library. For example, Zotero doesn't know if

• Jeff Smith
• J. Smith
• J. R. Smith

are all the same person, and treats these different names as different individuals. To prevent this from occurring, you can either go through your library and change all the names that refer to the same person to the exact same form, or you can use a style that doesn't try to disambiguate in this case. A step-by-step guide to completely removing “given-name-disambiguation” from a CSL citation style can be found here.