Google Sheets "COUNTIF" function NOT showing multiple conditions - google-sheets

I have a question about a google sheet formula?
=SUM(COUNTIF('Signed Case'!C:C,{"Barry","Maya"}))
It seems that Google Sheet can only count the total number of "Barry" but NOT BOTH "Barry" and "Maya", is there a way to fix this?
Greatly appreciated, thanks and have a nice day!

Change as
=sum(ARRAYFORMULA(COUNTIF('Signed Case'!C:C,{"Barry","Maya"})))
ARRAYFORMULA will develop countif for all criteria

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