So I searched online to find the government department responsible for this campaign, but found only what seems to be a loose-knit civil disobedience movement trying to hinder the authorities by telling people that writing a name on a birth certificate somehow grants the sole rights on that name to the government and not the individual, so the individual must not answer to it and therefore must not pay bills or fulfil legal requirements addressed to it. This message is embellished with symbolism to disguise it from less-persistent readers, such as employees of advertising agencies who might be less likely to let it through if it were stated more clearly. (I'm surprised they didn't claim to be "clay" that won't mix with governmental "iron" in the world-power prophecy at Dan.2:42-43, but perhaps that would give the game away too much.)
As of 2016, the copyright of a UK birth certificate applies only to its layout, not to the name on it, and the established authorities not only permit but often require a person to use the legal name assigned to them; its use might be illegal from the standpoint of that movement's interpretation of law, but such a standpoint is not currently used by the authorities and therefore is not the one to worry about with regards to visa applications etc at this time.
I will not take sides on the issue of the movement's free speech, but it might have been nicer if their alarming billboard had been placed somewhere other than the dangerous road junction I was trying to cross. I survived and was able to find the explanation a couple of hours later, but it was a big worry and could easily have been worse.
And if the government wants to use billboards for a public-awareness campaign, I hope it now differentiates itself so we know it's not another private interpretation.
(By the time we crossed that junction again in 2017, the "legal name fraud" advertisement had been replaced by another advertisement which was not related.)