I had to report this question because it does not accept "This name does not exist". I think it's correct, and I'd like to be corrected if it's not. Here are my thoughts.
Not only this sentence features this problem, but a lot of phrases in the Czech course that include "Ta" and "To" are not accepting "This" as a correct translation. It is confusing for me. Being a non-native English speaker, my first guess of such kind of phrase would be with "this" instead of "that". I really don't know properly how Czech is in this regard. But there are some things that make believe that I'm right. For example, one of the given translations here to "To" when we point at it is "this". I'm hopefully waiting for an answer!
This course does not accept "this" as an equivalent of "to" but as an equivalent of "toto" (which has colloquial form "tohle").
ten/ta/to = that
tento/tato/toto etc = this
This DL course is quite consistent about this