No, the names are there in the file, streets included. Their default styles did not support the languages we needed out of the box (everything was shown in the local language or English IIRC), but it was easy to fix by patching the style. I don't remember the exact fix, but it was about as simple as replacing something like `["get", "name_en"]` with `["get", ["coalesce", "name_xx", "name_en"]]`.
Is there enough information to show exact addresses? For example "221B Baker Street"