Yes the third generation does seem difficult as even in america the first year it was badged as a Civic del Sol but after the first year the Civic badge was dropped (although I have to study some official literature from Honda as it maybe the same situation as the second gen where the civic badge was gone but the car was still refered to as a civic crx in literature)

For cars sold in the usa it is easy for the 1st and second generations They are all "Civic CRX" with the trim designations of DX, HF or Si. So I think that is how we should list them