Can I be sued if my name is not on a lease?

If your name is not on the lease, you do not have privity of contract with the landlord, and would unlikely be sued by that party. However, if there was an agreement between you and the former boyfriend that you would contribute a regular amount towards the rent, in exchange for staying there, it is possible that the former boyfriend would seek sums owed up until you left. Nevertheless, his kicking you out occasioned your departure, so that weakens his argument that you are "breaching" whatever informal agreement you two had. More facts might change my analysis, but it does not appear that you have strong reason to fear being sued. Be careful about these kinds of unpleasant potentialities the next time around.