Naming ionic compounds with multiple cations and anions
I propose you consult the recommendations of the International Union of Applied Chemistry (IUPAC), in particular the Red Book as reference.  Obviously, you deviated for a reason from the Hill formula of $\ce{NaKCl2}$ (that were $\ce{Cl2KNa}$) some data bases adhere to.

As already presented in rules IR 4.4.2.1, and IR 4.4.2.2, the order of the elements within the formula may be arranged either by their relative electronegativity (starting by the element of least electronegativity), or by alphanumeric order, respectively.  So rules in section IR 5.4 subsequently discriminate between electropositive constituents to be named prior to electronegative ones in the "overall name".  In addition (quote):

"The order of citation is alphabetical within each class of constituents (multiplicative prefixes being ignored), except that hydrogen is always cited last among electropositive constituents if actually classified as
an electropositive constituent."

The same reference provides numerous examples of application useful to look at, too.  Page 76 (of the book, not the pdf) is a good place to start.  As in nomenclature of organic compounds, there are instances you want to point the attention not only to the stoichiometric composition of the compound, rather than to different constitutional isomers.