We consider near horizon fall-off conditions of stationary black holes in Einstein-Maxwell-Dilaton theory and find conserved charge conjugate to symmetry generator that preservesnear horizon fall-off conditions. Subsequently, we find supertranslation, superrotation andmultiple-charge modes. We apply the obtained results on a typical static dilaton black holeand on a charged rotating black string, as examples. In this case, supertranslation double-zero-mode chargeT(0,0)is not equal to black hole entropy times Hawking temperature. Thismay be seen as a problem but it is not, because, in Einstein-Maxwell-Dilaton theory, wehave a U(1) gauge freedom and we use an appropriate gauge fixing to fix that problem. Weshow that new entropy formula 4πˆJ+0ˆJ−0, proposed in [5], is valid for black strings as well asblack holes
