Thady \th(a)-dy\ as a boy's name is a variant of Thaddeus (Aramaic), and the meaning of Thady is "heart".
The baby name Thady sounds like Thad, Teddy, Tad, Tadd and Tadi. Other similar baby names are Thandy, Thano, Chad, Chadd, Shad, Shadd, Shadi, Shade, Shaday, Tay, Thandey, Thane, Thaw and Thoby.