With Frontier, it does. `Customers of size` are even required to do so. I travel with used to travel with a large service dog and the one time I flew Frontier with her I put in the name of my dog (who hashad a passport ) in the reservation and then called to say I needed the seat so the dog could fit (this was back in the day when this was still possible). No problems.
How to do this today? I`d put your name and "extra seat" in the reservation and then use the chat tool to contact reservations so this can be properly entered into the reservation system.

BTW, i routinely bought two seats when flying on carriers like Frontier who don't offer enough space for the dog to fit in front of me (or when premium cabin seats were prohibitively expense or sold out on airlines who do).
Outside of the US where the legal framework differs, airlines can and do require the purchase of a second seat for the animal should it not fit within the space allocated by one seat.