Columbus had begun his project at least from 1479 when he moved to Portugal, he entertained correspondence with a florentine man named Paolo Toscanelli, a geographer whose' theories allowed Columbus to plan out the daring voyage.

To fund and sponsor his expedition, he had asked the king of Portugal first (unfruitfully) and then he appealed twice to the consort sovereigns in Spain, once with a negative answer in 1486 and a second and successful time in 1491.

Now, even if the expedition had been sponsored by the monarchs the actual financial funding was not entirely a kingly matter, (edit, this next section was edited as I had trouble corroborating the total amount of florins needed for the expedition) in fact a great amount of the funds were advanced by a Genoese man named Francesco Pinelli and some florentine bankers. The ships and crew were spanish though and as such the expedition was always intended to be "claimed by the Spanish monarchs"; that's why the place they landed in America was named "San Salvador" and not "San Salvatore" as it would have been in Italian.

The land was claimed as Spanish, Columbus himself wrote in Spanish in his diary and he sent letters to the monarchs to keep them informed; the claim was very much taken by the Spanish from the start.This does not mean that there was any intention to steal off of Columbus the "prestige" of coming up with the idea; he was the captain of the expedition, he had worked and planned the project for decades, he was a great sailor (the feat of crossing the Atlantic is not an easy one, no one had tried before at those latitudes and as such there were many strange maritime phenomena that he couldn't have known of).

In fact his return was greatly celebrated, even the king of Portugal offered him help to return to Spain (since he had landed in the portuguese Azores on his first return trip).What I'm trying to get at is that he was very much a celebrity for this act and anyone interested in his expedition would have known it was pretty much his idea.

While being appointed as governor of these new Spanish land, eventually the general disappointment in the fruits of his later expeditions and, most importantly, the accusations of tiranny and brutality led to his downfall. He was quickly stripped of his governatorial role and, along with his family, was even arrested for a time.He never ceased to defend himself against the accusations until his death.

In conclusion I'd say that there was never any desire to pretend that it had been a Spanish idea in the first place; I don't know that "Spain" (along with all other "nations" in Europe) even existed long enough for this desire to exist. The man certainly died with a tainted reputation but not at all forgotten.

Sources:
Aurelio Musi, "Le vie della modernità" (the ways of modernity), 2018

Gianni Granzotto, "Cristoforo Colombo", 2010

Marianne Mahn-Lot, COLOMBO Cristoforo in "Dizionario biografico degli italiani" (Biographical dictionary of italians) vol. 27, 1982