Likely a variant of Adriana, from Hadrianus meaning from Hadria.
Edrianna is likely a modern variant of Adriana, ultimately from Hadrianus and the ancient place name Hadria. That ancestry gives the name an old Roman foundation beneath its more elaborate modern surface.
The extra initial E changes the rhythm and makes the name feel more individualized, as though it has been expanded into something slightly more ornate and contemporary while still retaining the recognizable core of Adriana. The appeal of Edrianna lies in its balance of classic and inventive elements. It sounds long, feminine, and stately, but it avoids feeling strictly traditional because of the altered spelling.
Names like this often feel appealing to parents who want the familiarity of established names without the exactness of a standard form. Edrianna suggests continuity with a classical past, but it arrives in a distinctly modern package.