Job title vs Skills

First, I'll give you some context, then will ask my question which is eating me a lot I recently switched from an Indian startup to a US-based startup. So, in my last organisation I was an SDE-2 (got promoted from SDE-1) and in my current organisation, which is an early stage startup, I have been given "Software Engineer" position, as there is only me and my manager currently. Skillwise, I am really good at tech, at managing, at team work, etc. So my question is, how much the position/title matters as compared to your skills? If position matters, then should I ask my manager to give me a better title for the position keeping in mind that it has only been 2 weeks in the new organisation?