Many times when you rent a "dedicated server" you will get a virtual server. You don't own the hardware and it can move from one server to another but you will not notice this. Licensing in this environment is cheaper sins the company owning the cluster is buying licenses based on cores. In that situation, you are most of the time not allowed to use your own sins the company selling this product has the final responsibility over that the hardware is running on correct licenses.
On the other hand, if you rent only space and bandwidth (own hardware, can be expensive as hell) or physical hardware from the company they might allow you to use your own.
I think that it is a dedicated cloud you are looking for as @dmurphy listed OVH has this.
Iaas cloud infrastructure 100% dedicated and managed by OVH. VMware vSphere virtualisation. Resources on demand. Professional solution.
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If it is possible for you I would recommend something like this to start with from your own home.
It saves the upstart cost (paying for a full server with no users on) while you developing the base parts of your server. The only requirement is that you have 10 MBit connection for it and you will be able to hold the first 40-50 players on your shard running. You might be able to get it up at around 300-350 dollars.