You open MLStyleDictionary via Database.MLStyleDictinaryId, and loop through each DBDictionaryEntry, the key of the entry is the MLStyle's name.
using (Transaction acTrans = acCurDb.TransactionManager.StartTransaction())
{
DBDictionary acLyrTbl;
acLyrTbl = acTrans.GetObject(acCurDb.MLStyleDictionaryId,
OpenMode.ForRead) as DBDictionary;
foreach (var acObjId in acLyrTbl)
{
MlineStyle acLyrTblRec;
acLyrTblRec = acTrans.GetObject(acObjId.Value,
OpenMode.ForRead) as MlineStyle;
acDoc.Editor.WriteMessage("\n" + acLyrTblRec.Name);
}
}