This is a reported problem, but JRiver has not fixed it yet.
When cue tracks are converted MC uses the filename of the source audio file (like MC normally does when a file is converted from a format to another format) and adds a sequence number to each new converted track file (for avoiding the files to overwrite each other).
The filenames would be easy to fix afterwards if MC would include proper file tags from the library data. Unfortunately it does not do that. MC copies the same identical tags from the source disc image file (if it has any tags) to each new track file.
MC has a mechanism for making correct file tags from the library data when untagged wave files (
*) are converted to other formats. MC should use the same mechanism when cue tracks are converted.
Currently the best workaround is to use APL files.
Personally, I rip all new CDs in APE & CUE format, then I make APL link files with MakeAPL (included with the
Monkey's Audio software) and tag these APL files with MC. MC has no problems with converting APL files to any supported format (the file tags are preserved).
Usually I convert them to high bitrate lossy track files (MP3, OGG or MPC) and keep these "APE & CUE & APLs" albums only in my offline lossless archive.
* The wave format doesn't have a common standard for tagging. Some programs may apply proprietary tags, but those are not usable with MC.