The red is frosting? As in buttercream? My guess is that it is an overlay. Ice the cake first in either buttercream or fondant and them do an overlay of red fondant with the letters already cut out of it. That would be my guess, but I have never tried it. Good luck!
Pam is right. I would crumb coat it, cover it in white fondant, roll out your red fondant, cut out the design, and then apply the red fondant over the white. I'm pretty sure that would be the best way.
I don't know if you cut out that much detail and then tried to stretch the red fondant over it you'd get it straight? When I did the Paris cake in my album (the one with Barbie on top) the cheese wheel is two layers of fondant. The circles were cut after the top fondant layer was put down. You could probably stencil it on and then cut it out with an exacto knife. Just make sure you don't cut all the way through the white fondant. Conversely if you had crusting butter cream and whole lot of patience you could stencil on the letters and then use a scraping tool and very carefully scrape away the interior?
You could cut the letters out of the red fondant and then put it in the freezer for 5 mins so that it will hold it's shape while applying it?
Perhaps the name is cut out with a digital cutter. Then lay the cut out name on the white buttercream.
Frost cake with thin layer of red buttercream.
Pull away stencil cut name.
Only job here would be to add small tabs to the cut out name so that it's easy to pull away.
You know looking at this photo, maybe what they did is they piped around the where the letters should be, piped in all the small crevasses and then just smoothed away the buttercream??
Both of these pics bring my Cricut to mind. In the first one with the red, the letters look cut out of fondant. A double layer of fondant, one white,and one red. Cut out my name on the red piece, but I wouldn't remove the lettering until I had the red piece on the cake.
In the second picture, it looks just the opposite to me. It does look like its been iced (although I'm not sure with buttercream), but the name looks to be cut with a digital cutter on fondant and applied over the icing.
Both cakes don't look like the same technique to me.
The second picture does look like buttercream or ganache, but how they did that I will never know! Good luck!
My guess is ...... the cake is iced in a thin fondant, the word is covered w/some kind of tape; the cake is covered w/the final icing and the tape carefully pulled off.
Think of how one would mask a wall when painting it and you don't want to get paint on the woodwork or want it in a special pattern.
I believe that the lettering was cut out, by exacto or digital cutter and carefully laid on the buttercream and using light pressure with a paintbrush indented into the icing. The icing would push up into the openings in the letters. That's what mine look like when I place letters on icing and press them into the icing.
This can also be a buttercream transfer... use acetate over your preferred lettering one color to write the word and another color for the overall layer.
Just a thought.