Im no doctor but wouldn’t logic dictate that once it jumps from Human to “turkey” the strain name would change. Now it effects a human and 2 animals, rather then 1 human and 1 animal. It had to morph in some fashion, thus its no longer H1N1. Perhaps the viri morphed and only attacks turkeys and cant jump from turkey to human, or pig for that matter. Just food for thought...
H1N1 describes the cell interaction characteristics. The ‘H’ helps the virus bind to cells before infection (hemagglutinin). The ‘N’ helps the virus release from the cell (neuraminidase). The species infected makes no difference as these (glycoproteins) remain the same. The H5N1 for instance has a different H configuration which is why it isn’t spread as readily in humans. The initial binding of the virus is less compatible.