If the lease is solely in your name, you could do a formal eviction of partner vs having to move out. The process varies by state and some cities. But usually you have to give at least 30 days notice and follow the legal steps for it to be enforceable.
What usually happens is that one or both parties moves out. The one that remains retains the lease and the one who leaves is quits (absent a prior contractual arrangement). If both leave, the lease is dissolved (ing to the terms of the lease arrangement).
They simply need to prepare a simple lease amendment that states that the parties intend to amend that certain lease dated XX between them and you & boyfriend and state that your boyfriend is hereby released from the lease and the lease is amended to remove all references to his name.
Adding someone to your tenancy means you both become joint tenants. It's not the same as passing your tenancy on to someone else. You need permission from your landlord to add someone as a joint tenant.
In most cases, it is possible and easy to add someone to an existing lease if it's allowed by the landlord. However, the landlord will need to write a lease addendum or lease amendment to add new information to the lease that can protect all parties.
What usually happens is that one or both parties moves out. The one that remains retains the lease and the one who leaves is quits (absent a prior contractual arrangement). If both leave, the lease is dissolved (ing to the terms of the lease arrangement).