What do we call linear maps from the base field to a vector space? This is just a terminological question for some notes I'm writing: Let $V$ be a vector space over a field $F$. A linear map $T:V\to F$ is called a linear functional.
What do we call a linear map $v\colon F\to V$? I'm inclined to call them cofunctionals, but I don't think this is standard.
[Linear functionals are also called "covectors". So maybe "cocovectors"? Then the natural identification $L(F,V)\cong V$ ($v\mapsto v(1)$) would identify vectors and cocovectors, which is nice.]

Edit: Just for motivation, these maps $F\to V$ are helpful for writing down general linear maps in terms of functionals and 'cofunctionals' (which are easy to deal with), and apply that to study ideals of linear operators, for example.
If $T:V\to V$ is linear with $dim(V)<\infty$, then $T=\sum_k (Tp_k)q_k=\sum_k p_k(q_kT)$, where the $q_k$ are a basis for $V^*$ (dual of $V$) and the $p_k$ are right-inverses of the $q_k$.
The $q_k$ and $q_kT$ are functionals, and $p_k$ and $Tp_k$ are 'cofunctionals'.
 A: There is a canonical identification $\operatorname{Hom}(\Bbb F,V)\cong V$ for any $\Bbb F$-vector space $V$. (Here $\operatorname{Hom}$ is the set of $\Bbb F$-linear maps from $\Bbb F$ to $V$.) The map is exactly as you describe and takes $f$ to $f(1)$.
So in my opinion, it would make sense to say linear maps $f\colon V\to \Bbb F$ are covectors and maps $g\colon \Bbb F\to V$ are vectors. However, there is not much to be gained here. It would just cause confusion, as we already think of vectors as elements in the underlying set $V$.
One thought I just had: this is only tangentially related, but one way to define the tangent space of a point $p$ in a smooth manifold $M$ is by equivalence classes of curves $\gamma\colon \Bbb R\to M$ (or $\gamma\colon(-\varepsilon,\varepsilon)\to M$ for any $\varepsilon>0$). The point is that a $\gamma$ represents the tangent vector $\gamma'(0)$ in the tangent space of $\gamma(0)$. It is not entirely coincidental here that we basically identify maps $f\colon\Bbb R\to M$ with certain vectors. (Dually, a map $g\colon M\to \Bbb R$ defines a covector at each point.)
