What is the name of the score a student would get if the measurements were completely accurate and error-free?

The correct option is True score.

In classical test theory, a student's observed score on any measurement is considered to be composed of two main components: their actual underlying ability (the true score) and some amount of measurement error.
This relationship is mathematically represented by the formula:
$$X=T+E$$
where $X$ is the observed score, $T$ is the true score, and $E$ is the measurement error.

The True score represents the theoretical value that would be obtained if the measurement process were completely perfect, accurate, and entirely free of any errors (i.e., when the error component $E=0$). Thus, if there is no measurement error, the observed score directly equals the true score.