There is no term for this because this is not how cryptanalytic attacks work.
Typically, attacks like these do not reveal that a key lies in a specific range, but that the secret material has certain properties. Finding those properties is part of cryptanalysis in general. As such, I don't think there's a specific name for this since it really doesn't exist. Things that don't exist or are very rare don't always have specific names. You need a description. In this case, you would describe an attack that shows you that the secret material has certain properties.
Here's a simple example: Let's say I created a password hash by taking the integer representation of the password, modulo 256. The hash is thus an 8-bit integer in the range [0,255], which is obviously too little. But do we have to brute force all possible integers (infinity)? No. If we know that the hash is the number 163, we can tell that the input is congruent to 163 (mod 256). This is enough information to instantly generate a candidate password that hashes to the same result, but it doesn't tell you what the original password was unless there are very few possible passwords to choose from.
Obviously such an example is too simple for real cryptographic algorithms (although there are real checksum algorithms which use this technique). What does such an attack actually give you? A set of properties that an input must have for the attack to work. Sometimes the properties are easy to meet and require very little computation. Other times they have unknowns that must be filled by brute force or which are so complicated that finding them actually takes nearly as much time as a true brute force of the keyspace. A trivial example (in the cryptanalytic sense) would be for finding colliding MD4 inputs. Instead of giving you a flat range from a to b, you get something like:
From the linked website:
It’s relatively easy to satisfy the first few constraints, but as you go on it becomes harder and harder because with each new constraint you have to ensure that you don’t mess up all of the prior ones. In our attack we satisfied all but 19 of Wang’s constraints and 1 out of the 2 additional constraints listed in the improved attack. This suggests that we need to generate 220 or around 1 million messages to find a collision. This seems to be borne out by experimental results.
I am not aware of any specific term that describes generating these 1 million messages other than, in this case, "MD4 collision attack". Note that this is not the best attack against MD4, and the best attacks have a complexity of less than 2. No, that's not a typo. It's 2, which is far less than 220. Attacks against better, modern cryptographic primitives which have a far higher complexity have even more complex conditions that must be met. Even MD5, which is considered fatally broken today, is far harder to break than MD4.
