I think "Unsay ngan/ngalan nimo" would be more appropriate.
Unsa is simply "What". In sentences, considering the use of correct grammar, unsa becomes unsay. "Unsay" is more like "What's ~ ".
And no, "imo" is not always shortened to "mo". Although I think you already know that the Cebuano speaking style tend to say things in shortcut like how "ngalan" is made "ngan". It's how Cebuanos normally converse.
"mo" can be a shortcut to several words that can have different meanings like "nimo", "kamo", "namo".
"imo" and "nimo" both mean the same thing, "you/your/s". You just have to be careful because in some cases, they cannot be interchangeable. In your example, the "mo" is the shortcut to "nimo" and not "imo".