There are a few names used to for this second choice of party vote under MMP.
Credit for the idea seems to beling with Germany, where the concept is apparently known as Ersatzstimme. This translates into English as Substitute Voice, so perhaps Substitute Vote, and perhaps Spare Vote.
The Wikipedia page describes Spare Vote as a form of preferential voting, of Single Transferable Vote. This seems to be incorrect, as the Spare vote involves making a second choice of party, to apply when a first choice party does not pass a threshold.
In contrast, Single Transferable Vote refers to voter placing candidates (perhaps with party affiliations) in order of preference. Determining a winner or winners involves applying an algorithm to transfer votes between candidates. There are various possible algorithms. STV has no connection with Ersatzstimme.
There is a German website dualvoting.com which uses the name Dual voting or Dual Level Voting. This name highlights that Ersatzstimme is a kind of two round voting with both rounds voted on the same voting paper. The first round the voter chooses a party. If that party passes a threshold, that same vote counts for the second round. If the party chosen at the first round does not pass a threshold, the voter has a vote in the second round.
I have explored various names for this idea, some from before I knew about Ersatzstimme. I have used ‘two-choice party voting’, ‘two-choice MMP’ and others.
However all the different names refer to the same idea. If a first choice party misses a threshold, that persons vote goes to their second choice party. I have wondered about using the name ‘Two-step party voting’.
Two-choice party voting or The Spare Vote 