This is a thread in preparation for the vote on the names. Meanwhile there are already many proposed names and the idea of this thread is that via people voicing reasons for their respective preferences we can perhaps find some conensus to exclude some, or perhaps group some together (and decide details in a second round).
Here is the current list, takesn from an answer by Jim Belck plus an addition be me (the final one).
Mathematics Learning, Studying, and Education (the current name)
Mathematics Teaching and Learning
Mathematics Teaching and Pedagogy
Didactics of Mathematics
Pedagogy of Mathematics
Mathematics Pedagogy and Teaching
An answer here should not be a vote but rather gving reasons to prefer one over the other, ideally discussing most or all the proposed names (see https://area51.meta.stackexchange.com/a/13104 for an example).