When I import my photos in lightroom, the ones taken with Sigma lenses does not show the exact model designation contrary to Canon lenses that are presented with the full information. On my sigmas only the focal length range is shown. It's not that lightroom doesn't know what lens it is though. If I apply lens correction the correct lens is detected.
Is there any way to get lightroom to write complete exif lens information, not just lens focal length range?
The EXIF lens ID information is written by the camera, Lightroom just displays what the camera has written in the 'Lens ID' field. The only field that Lightroom allows the end user to edit is the 'date/time' field. But the lens correction selection is something that Lightroom does itself and apparently it can use other clues besides the EXIF Lens ID to tell one lens from another. For instance, since the Sigma 70-200mm F2.8 EX DG Macro HSM II and the Sigma 120-400mm HSM apparently have the same lens ID number, if the reported focal length at the time a photo was shot might be 300mm, Lightroom is smart enough to figure out which of those two lenses was attached to the camera. Even where there is overlap of the focal length range, the different maximum apertures of each lens might be used to differentiate which lens it is.
Sigma has a history of reusing the lens ID across different lenses and so correct identification of them is actually quite tricky in some cases. I would not assume that the lens correction feature is actually working properly, though it may be using some additional information to figure it out and so generally works. However, that doesn't help when it's just displaying the EXIF data to you which is what it is doing on import.
