Is there a name for a local homomorphism $\varphi:A\longrightarrow B$ of local rings $A$ and $B$, whose completion $\hat{\varphi}:\hat{A}\longrightarrow\hat{B}$ is a finite homomorphism? (that is, $\hat{B}$ is a module finite extension of $\hat{A}$ via $\hat{\varphi}$). Perhaps formally finite?

Is there a name for a local homomorphism $\varphi:A\longrightarrow B$ of local rings $A$ and $B$, whose completion $\hat{\varphi}:\hat{A}\longrightarrow\hat{B}$ is a finite homomorphism? (that is, $\hat{B}$ is a module finite extension of $\hat{A}$ via $\hat{\varphi}$). Perhaps formally finite?

EDIT: Assume $A$ and $B$ are Noetherian.