Is there a name for a boolean operator whose value always equals its left-hand side operand?

Question

Given a binary boolean function with truth table as follows:

|-----------|
| 0 | 0 | 0 |
|---|---|---|
| 0 | 1 | 0 |
|---|---|---| 
| 1 | 0 | 1 |
|---|---|---| 
| 1 | 1 | 1 |
|-----------|  

I am wondering if this function has a name in academia?

Answer 1

In general $f(x_1, x_2) = x_1$ is called "projection onto the first factor."

Answer 2

Projection or identity.

In general, a function that returns the $m$-th of its $n$ arguments is written as $id^n_m$

So your boolean function would be would be $id^2_1$, and thus $id^2_1(P,Q)=P$