People tend to gravitate to Zoro since he was the first to join, consistently the 2nd strongest, one of the members fairly vocal about chastising Luffy's poor decisions and offering a strong opinion on matters of the crew such as whether or not to accept Usopp back. Despite that though, I'd say Nami has more right as a 2nd in command of sorts as Zoro lacks any role in the crew beyond fighting, whereas Nami's navigation skills and ability to give orders properly is the most important to the crew's survival at sea overall.
The real answer is that there is no true "first-mate" of the Straw Hat crew, considering Luffy treats everyone as equals rather than it having a clear hierarchy like with other Yonko crews, with Rayleigh being the only person thus far known to have the title of first-mate on a crew.