As the error message states, the format OGC Geopackage does not support labels as such. You’ll need to create a Point-feature, with an attribute “label” or “name” or something to contain the text of the label. It is then up to the client software to display that properly. If the labels also contain positional info, such as rotation, font-size, displacement, etc, you’ll also need to create attributes for that information, if you want that stored in the geopackage.

Thanks for the quick answer.

I managed to export labels to geopackage file via GeoMedia Application. 

So what do You mean by “the format OGC Geopackage does not support labels as such”? Is that mean that FME geopackage writer does not support labels? 

mean that FME geopackage writer does not support labels? 

Yes, that is exactly what it means. The Geopackage format does not support labels as a datatype, so the FME Writer can’t support it either, because there is nothing to write it to. That is also what the error message already said: “Unsupported geometry type Text.  Downconverting to Point” .

It’s the same as trying to write geometry to an Excel, that also won’t work because it is not supported by Excel (although in that case you won’t get an error message). So if you still need all the label-specific information, you will need to add that yourself, or choose a different format to write to that does support labels.