Hi Alex,
If you want to completely disable registrations on your website, you can go to Settings > General and untick the “Anyone can register” checkbox. Doing this should also remove the register button in your navigation bar.
If you only want to hide that button without disabling registrations, by default there’s no option for this but as a gesture here is a CSS code snippet that will hide it :
#navigation .nav.navbar-nav.navbar-nav--login > li.menu-item--register {
display: none;
}
To use this CSS snippet, open the customizer by going to Appearance > Customize, then open the Additional CSS panel, paste the snippet there and publish.
Hope this helps !
Best regards,