It... depends.

In the lore of the book, the company Nike would not give a true "worship" to the goddess, as in prayers or ritual or sacrifices. There is nothing victorious in all that, they merely use her name. It is not like for Ostara where her holidays and celebrations are reused, even though nobody knows who she is. So the most the company Nike can do is spread the name of the goddess in a sort of "fame".

But in the Hall of Forgotten Gods, we see that even gods whose names and stories are remembered and recorded can die if they do not have enough worship. For the name to be known is not enough - especially since when people speak of Nike they often think of shoes, of the company, rather than the goddess. It can maybe help her survive a bit (the same way for exemple it is implied that Odin can survive thanks to being one of the most well known members of his pantheon) but even that is not enough, and just like Mr. Wednesday she would need aside worship.

That being said, in the television series, it is possible that Nike "updated" or "upgraded" by making a deal with the New Gods and having the company started in her name. It could give her a form of worship and energy. And I do not know the work ethics of the company, but if they use sweatshops or the like, this adds pain and sacrifices to the worship.

Basically an "indirect cult" is only useful to the Old Gods if this repeats their rituals. Easter's holiday is the best exemple of an indirect cult: her rituals, symbols and practices, her holiday, is repeated massively throughout the United-States, but with no one intending for it to be a worship, and nobody thinking about the goddess Ostara when doing it. It gives power to Easter, it allows her to survive and not fade away - but it is not enough. She doesn't have her full divine glory, she is still quite weak (and in the novel we see that she is prone to depression, and feels ultimately quite tired of what seems to be a pointless existence).

But for just a company to share the goddess name... it doesn't really count as a worship. Since there is no true ritual, prayer or veneration involved.

(Except again if we are in the television series and Nike could have accepted a deal like how the New Gods offered Odin a nuclear missile in his name to become a god of nuclear warfare)

it is the same for the symbol of medicine (asclepius) and a more direct cult is the parthenon of nashville (Athena). or Saint Valentine (Cupid - Eros) and the triple goddess of Wicca Hecate

For the symbol of medecine... I do not know. Technically speaking, the Caduceus used for medecine can either be the one of Asclepius or the one of Hermes, and even then it is merely the use of the symbol. I do not think there is much worship there (though there might be but it is hard to tell given that Asclepius is not among the Old Gods brought to America). There is also the mention in the novel that among the New Gods are those of hospitals, so in the novel lore it seems medecine is under the thumb of the New Gods

Saint Valentine's Day has no actual cultural ties to Cupid. Cupid became a mascot for it, true. You could say that in the television series lore Cupid maybe made a deal with Media (the same way St. Nicholas made one to become Santa Claus and Ostara made one to become Easter), but honestly I am not sure.

The Nashville Parthenon? Definitively not in the book (it would probably be one of those "fake" places of power, the same way for exemple Disneyland, as explained by Wednesday, has no true power - the real places of power are roadside attractions, not centers of tourism). In the television series maybe Athena would draw a bit from that (the same way the Egyptian gods somehow got a bit of hold thanks to Laura's casino) but that is very debatable and certainly not enough for Athena to survive.

After that, it is really quite difficult to speak of this very theorical subject. Indirect worship of an entity is certainly not what a go will look primarily. Before anything, they will look for a way to have "direct" worship in an "indirect" way (sexual partners for sex magic, victims for sacrifices, corpses for funeral rituals, occassions for their rituals and holidays to be celebrated). Just having a building at their name or their symbol used doesn't mean much. Sure it can feed a bit, but not enough (the same way Odin, while due to his fame can last a bit, he still needs from time to time young virgins to "freshen" himself up)

I remember the Olympic games its celebration ( ritual )in honor of Zeus and the gods. & The caduceus the symbol of hermes, Caduceus is a symbol with a short staff entwined by two serpents, sometimes surmounted by wings while the Rod of Asclepius is the one with a single snake.

Yes. But as I said, just using a symbol isn't enough to be considered "worship"

As for the Olympic Games, they are not a purely American tradition.

The Olympic Games can count as indirect worship. But only when they happen in the United-States (since again, we are talking North America here. The gods in the original homelands are a whole different subject that we don't know much about)

I think the Nike one could be good if you examined it from a similar standpoint to how Jennifer Government viewed the company, i.e. that a key part of their business model was making Nike shoes something so fashionable and so expensive that they were a thing people would kill for. That would give you the worship and sacrifice portion. They kinda did a similar thing in the show with Vulcan's gun company, where people worshiped the gun and it transfered to him.