Why do we call complex numbers “numbers” but we don’t consider 2-vectors numbers?
They're called "numbers" for historical reasons, since the motivation in the development of the complex numbers was solving polynomial equations. They were viewed as natural extensions of the real numbers. It's somehow quite natural and satisfying to say "every polynomial equation can be solved by some (complex) number". Is it more natural to regard $i$ as being a number which, when squared, is equal to $-1$, or is it more natural to regard $i$ as being some non-number thingamajig which when squared is equal to $-1$? Clearly the former.
"Higher" number systems, like quaternions, aren't really called numbers very often, for the simple fact that they are not as intimately connected with number theory and analysis in the same way that complex numbers are.
Beyond these social conventions, I can't see any other reason. The word "number" doesn't have a strict or absolute definition in pure mathematics. $\mathbb{N}$, $\mathbb{Z}$, $\mathbb{Q}$, $\mathbb{R}$ and $\mathbb{C}$ are technically just sets with a certain algebraic structure.
I partially disagree with the other answers which claim that complex numbers are numbers simply by virtue of the fact that you can add and multiply them. Well, if that's the rationale, is every ring also a set of numbers?
The two fundamental operations for numbers are "addition" and "multiplication" which obey very nice "laws" of arithmetic. Taking powers is also important. You can do all of those things with complex numbers. You can add two vectors but the "dot" product of two vectors is not a vector and the "cross" product of two vectors does not satisfy the "nice laws". Neither the dot product nor the cross product of vectors can be used to define powers.
I think naming is a rather soft topic, so there may not be a hard answer. However, I think it is worth noting that complex numbers are one of the three associative real division algebras (real numbers, complex numbers, and quaternions). These are all linked by the idea that division is meaningful in those three systems.
In general, a 2 dimensional real vector cannot admit a concept of division which matches what we expect division to do. However, if said real vector defines addition and multiplication the way complex numbers do, division is a natural result of those definitions.