Is there a name for the pattern of matching two things by using a line to connect them together?
This is often used on school tests that try to match a word with its proper definition. Here is an example:
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Sign up to join this communityIf a new term is needed (as there doesn't appear to be an existing one), I would suggest calling it a Patch Panel. This is the term for the physical counterpart, common in networking, where "patch leads" can be connected between sets of sockets. See, for example, following image (especially the right-hand portion):
Source: This product page on Amazon found at random through image-search (no affiliation).
I like patch panel as suggested by TripeHound. But perhaps an older technical analogy is even better, the telephone switchboard:
A little more explanation of the terminology on Etymology SE Where does "patching through" come from?
The "line to connect from one side to another" with all sorts of crazy diagonals depending on exactly what is needed, fits a telephone switchboard precisely. That is actually more than with a typical modern network patch panel where many technicians will try to wire things up, at least initially, so that most patch cables are straight (horizontal or vertical) instead of jumping all over the place.
Because you mention school, I just wanted to add that this was always called a "mix-and-match puzzle" in my classes. This would specifically mean the words, and definitions, are purposely jumbled to create a puzzle.
For your purposes, however, I wouldn't use this term because it would imply it is a game. I second the "patch panel" in this instance, as that makes it clearer that they are simply making choices in format.
You could also dub it "Pairing Pattern" (or "matching pairs" as said by @Rahul). Since you are linking pairs of elements from two sets.
This is a "Word-Definition Matching Widget"
(Full transparency: I just made that up after googling it and finding a bunch of examples on worksheets meant for paper)
I think there isn't an easily findable name for this pattern because it doesn't translate to the web very well. I'm trying to imaging what the responsive mobile version would look like and I can't.
Doesn't roll off the tongue, but this is a bipartite graph or diagram - this covers the possibility of one to many links as well as just pairings
See the very similar diagrams to your example here --> https://www.google.co.uk/search?q=bipartite+graph&tbm=isch
matching-pairs