yes, okay, they can, but they will only be like usual vouchers. They will never be able to create a currency accepted by other companies.
However, they can "sponsor", and that is just what Elon has done, setting himself up as a kind of godfather of Dogecoin or honorary president. So he already has "his own" currency
This is how it could happen, not that it would be used by other companies but if a place like google or facebook or apple or anything else creates their own token then they could make you use it, as an alternative of course, you can still use dollars, but you could use their tokens as well. That is the most important part and that is what I believe should be the case whenever they create a new coin as a company. It is not the perfect version, but not terrible neither.