Do you have a sample DGN file for me, maybe?
The Microstation cells may contain Enter Data fields, which is a special type of text that can contain user added text. When written to the same block name in DWG, one copy of the cell is used to define the block, and instances of that definition are placed at the cell locations, all with the same label.
To fix this, you need to aggregate each cell's elements into a single feature, then use a GeometryPartExtractor to remove the text geometry from the aggregate. The text contents will still be available as the attribute 'igds_text_string'. Create a visible attribute on the output block to store the text contents. This will allow you have a different label for each instance of the block.
I would be happy to give you a more detailed explanation and a sample workspace, if you would like to send a copy of your source dataset to support@safe.com.