Sublime Text was useful in the early stages, when the product was getting known.
It helped understand quickly the purpose of the software.
Now, it fairly well known, it could use better style.
I think dropping the Text and calling it just Sublime it justified.
You could leave the website domains the same, leaving the official name the same.
Just change the visible title in the forums, website, application executables, etc..
Customer support service by UserEcho