Citing own results which were obtained under former name
Theorem (Y. (under Formername), 2016)


Is fine. (I have personally never seen a paper that state[s one's] own results using only the initial. I presume it is specific to the OP's discipline.) Alternatively, Theorem (Y. (formally Xxx), 2016) or my preference:


  Theorem (Xxx (now Y.), 2016)


I favour this option because the bibliography will contain Xxx (2016), not Y. (2016). (At least, it won't unless you modify the bibliography.)