If Marc hadn't taken up politics, he might have __________________________ himself as an art historian.

The phrase "made a name for himself" is a common idiomatic expression that refers to achieving recognition or a reputable standing in a particular field. In the context of the sentence, it suggests that if Marc had pursued a career in art history instead of politics, he could have become well-known or esteemed in that arena.

Using "made a name for himself" fits perfectly with the hypothetical nature of the statement. The structure established by "might have" suggests that this could be a potential outcome, which aligns with how the idiom is typically used, conveying a sense of achieved identity or status.

Other options do not convey the same meaning as effectively. "Lost a name for" does not work contextually, as it implies a negative outcome rather than recognition. "Developed a reputation" could suggest some level of acknowledgment but lacks the strong connotation of success embedded in "made a name for." "Gained recognition," while it hints at approval or acknowledgment, does not encapsulate the sense of personal branding or achievement inherent in making a name for oneself. Therefore, the idiom provides the most precise and contextually appropriate completion to the sentence.