Your investigation into Lorenzo Mascheroni’s role in the history of Euler’s constant $\gamma$ led to the correct conclusion. An authoritative historic and survey article on Euler’s constant is given in Jeffrey Lagarias’ paper “Euler’s Constant: Euler’s Work and Modern Developments” October 2013 Bulletin of the American Mathematical Society, 50(4), 527–628. If you haven’t already read Lagarias’ article, Mascheroni’s contribution is discussed in Section 2.6 on pages 555-556, and the article states that he merely contributed four more correct digits to Euler’s computed 15-digit approximation (but Mascheroni’s published expression contained 32 digits).
Lagarias mentions that at that point in history, it was not uncommon to name constants after the person who had gone through the “... labor of computing them to the most digits.” Lagarias’ historical exposition is quite detailed, and it seems unlikely that he would have omitted any more significant contribution that Mascheroni might have made regarding $\gamma.$ Given this, he says that it's probably most appropriate that $\gamma$ be named for Euler alone.
But if it turns out that the Grothendieck constant $k_R$ is the reciprocal of $\gamma$, I think that might warrant a hyphenated appellation. :)