Here’s a stitchalong video of how I generally stitch the names, first with the main color, then with the accent color.
This shows me stitching the classic lettering in Scarlet & Wine, but the same principles apply if you’re stitching a different color way or a different lettering style! 
I stitch one letter at a time and one color at a time. 
I tend to tie off between letters, just to keep everything super crisp. I think it’s especially important to do this if you’re stitching a name with a white background. It’s less important if you have a dark background behind the name because the thread tails are unlikely to show through. 
To keep things easy for myself, I just always tie off between letters 🙂
Stitching Your Name
 
       
    