Let's say there is a qubit at position $i$, and I want to move it to position $i'$. Without loss of generality, let's say $i < i'$. By 'move it' I mean, perform multiple $SWAP$ operations so that every qubit at positions $i<j<i'$ is moved over one position, so that they are moved to position $j' = j - 1$, and the qubit at position $i$ is moved to the qubit position $i'$.
This would be implemented using $i' - i$ number of $SWAP$ gates. Denote $SWAP_{k,k+1}$ as the $SWAP$ gate swapping qubits at positions $k$ and $k+1$. In Python-style pseudocode, this would be the way to implement the gate I am describing:
for k in range(i,i'):
SWAP(k,k+1)
I feel like there should be a name for the gate I am describing. If not, I want to call it something like $MOVETO_{i,i'}$ or $SHIFT_{i,i'}$.
Any suggestions?