Hi Snoop
If it is both you and your wife setting up a business you will have to register as a partnership. The reason being is that as a sole trader, only one of you can register the business. As a partnership, you can both put your names down as the owner of the business. A sole trader and partnership are pretty much the same thing except a sole trader is registered by one person, a partnership is registered by two or more people.
You do not need to have a premises to register as a partnership. Your home address will suffice, but when the time comes that you do have a separate premises, you will then need to change the address with the Companies Registration Office, so they can issue you with a new certificate to display in your new premises.
In relation to registering the same business name twice, yes thats no problem, but you will need to register it again showing a different address. The reason being, is that when you register as a partnership / sole trader, the companies registration office will send you out a Registration of Business Name certificate. This certificate must be displayed on your premises and will have the name of the business and the address of the business on it. Therefore if you have two businesses at two separate addresses you will need to register twice with CRO.