Anything is possible, but I’m not aware of any reliable evidence to support this idea. It is worth considering, though, that the histories of both Philo and Josephus portray Pontius Pilate as a man of great cruelty and insensitivity to Jewish customs. It would not be surprising if the Jews, or even the Roman government (in the interest of maintaining the peace), tried to erase the memory of his rule.
To give you an idea of Pilate’s temperament, I’ve included an excerpt from Philo’s On the Embassy to Gaius:
But when [Pilate] steadfastly refused [the people’s] petition (for he was a man of a very inflexible disposition, and very merciless as well as very obstinate), they cried out: ‘Do not cause a sedition; do not make war upon us; do not destroy the peace which exists. The honor of the emperor is not identical with dishonor to the ancient laws; let it not be to you a pretence for heaping insult on our nation. Tiberius is not desirous that any of our laws or customs shall be destroyed. And if you yourself say that he is, show us either some command from him, or some letter, or something of the kind, that we, who have been sent to you as ambassadors, may cease to trouble you, and may address our supplications to your master.’
But this last sentence exasperated him in the greatest possible degree, as he feared least they might in reality go on an embassy to the emperor, and might impeach him with respect to other particulars of his government, in respect of his corruption, and his acts of insolence, and his rapine, and his habit of insulting people, and his cruelty, and his continual murders of people untried and uncondemned, and his never ending, and gratuitous, and most grievous inhumanity.