Given that you have the ObjectId of an mleader...
Open that ObjectId and cast to MLeader. The MLeader.MLeaderStyle will get you the ObjectId of the style. Open that, cast to MLeaderStyle, and read the MLeaderStyle.Name property.
untested:
private void PrintMLeaderStyleName(ObjectId mleaderId)
{
Database db = mleaderId.Database;
using (Transaction t = db.TransactionManager.StartTransaction())
{
MLeader mleader = t.GetObject(mleaderId, OpenMode.ForRead) as MLeader;
MLeaderStyle mleaderStyle = t.GetObject(mleader.MLeaderStyle, OpenMode.ForRead) as MLeaderStyle;
Editor ed = Application.DocumentManager.GetDocument(db).Editor;
ed.WriteMessage("that was a {0}.\n", mleaderStyle.Name);
t.Commit()
}
}
