This would depend on how deep the neck cyst is located. There are skin cyst like sebaceous cyst that are superficial and can be treated very easily.
There are deeper neck cyst that may require surgery.
These neck cysts are usually due to congenital developmental brachial cleft cysts. These can be imaged with contrast X-rays and can be excised in its entirety. It might be prudent to consult an ENT specialist soon.