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I have an interactive regresison model as below:

$Y_{i,t} = \beta_0 + \beta_1$$D_i$ + $\beta_2$$P_{i,t}$ + $\beta_3$($D_i$$P_{i,t}$) + other covariates + error terms

In this model, why $D_i$ is called as the moderator for the relationship between $P_{i,t}$ and $Y_{i,t}$

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Because moderator variables are by definition variables that affect the strength of the relationship between one variable and another variable, and that is exactly what interaction effect does (it allows $P$ to have different effect depending on whether $D=1$ or $D=0$).

This is actually not terminology used widely in economics, but it is used widely in psychology and some other fields (although I seen it used in few behavioral economics papers). In economics, outside few specific subfields people usually call it interaction term.

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