There is not, however, a semi-formal version of the CSU as I have seen in a few pics around the planet.
There actually is, although it will be phased out along with the CSU.
The last sentence of paragraph 3.d (Corporate Service Coat) of the 28JAN08 ICL
reads: "This coat may also be worn with a black bow tie on formal occasions when the mess dress would be worn."
Since I don't see an instruction to remove the name tag when worn as such, I believe that makes this the only semi-formal variant to be worn with a name tag.