Yes, the change in the sign could be due to including (and controlling for) social desirability in the regression analysis. The regression coefficient is then a partial regression coefficient (partialling out social desirability). The previously significant (?) bivariate relationship between optimism and perceived stress going to zero (or close to zero) in the multiple regression model could mean that there is redundancy (i.e., optimism may not explain unique variance in perceived stress above and beyond what can be explained by social desirability).

Relationships switching signs between bivariate and multiple regression analyses can also sometimes point to suppressor effects (e.g., when the predictor variables are strongly correlated).

Another explanation may be differences in sample size between the bivariate correlation analysis and the regression analysis with all three variables combined (i.e., if there is any missing data).

I would carefully examine the bivariate correlations between social desirability, optimism, and perceived stress to better understand what happens in the multiple regression model when all three variables are included and check for missing data that may account for potential differences in the sample size and composition between the bivariate correlation analysis and the multiple regression analysis.