Is it possible to access an iPhone and send texts remotely, using that number?
Not sure "hacked" is the right way to describe it. To me, the most obvious way is if you have set up multiple devices (iPhone, iPad, Mac) with the continuity function that allows SMS texting across the devices... then you walk away from a logged in device (Mac?). That routinely happens at family events around my house - kids pranking their siblings - but that's easily preventable by locking/password protecting your devices.
As D said, it's not at all likely someone who has no physical access to any of your devices can hack in from a remote location with no prior access to any of your devices. Of course, bad internet habits, weak passwords and similar sloppy habit could go a long way to make things easier for the bad guy.