It is an interesting topic for debate.
If a lay person uses a Pali Name or any Pseudonym for posting on forums, is he or she guilty of breaking the fourth precept?
If a lay person chooses a name like Ariyavamsa, is he or she claiming to belong to the clan of the Noble Ones? That is, does it amount to a false claim to the status of an Ariya? Probably not, but it would depend on the motivation when choosing a name for oneself. I know a lay Buddhist called Gotam Chakravatti. I doubt if he is from the Buddha Gotama's clan, nor a world-ruling monarch, but then I expect that was his name given to him by his parents at birth. As far as I know, it is his real name. He is not just using it to be pretentious.
When monks are ordained, their name is chosen by their preceptor. In Burma the tradition is to choose a name depending on the day of the week on which they were born. They don't choose the name for themselves. It may be chosen to give him something to aspire to become — for example, like Karunabodhi = compassionate and enlightened. Pesala means "well-behaved, modest."
In the Buddha's time, of course, the laity had Pali names —
Anāthapindika = Feeder of the Poor, etc. This was an acquired name — his given name was Sudatta.
Devadatta = gift of the gods was a name given at birth. After ordination, he was still known as Devadatta.
Angulimāla = Finger Garland was a name given by the general public due to his custom of wearing a garland made from the fingers he had severed from his victims. He also retained the name after becoming a bhikkhu.
Sāriputta = son of Sāri, etc.
I don't see any great harm in choosing a Pāli name if one wishes to adopt it for religious reasons. A devout lay person might wish to be known as Sanghamitta, for example. However, I think there is a problem with using a false name for the sake of secrecy. Some of the so-called Buddhists on forums aim slanderous remarks at bhikkhus like a sniper or thief using darkness to conceal his actions. In this case, if that is the purpose, then definitely it is not suitable to use a false name, even less so a Pāli name that carried some kudos due to its meaning, or due to the good reputation of the former owner of that name in the Buddha's time.
These are some points to consider. Why not use your given name? What would you write on a Buddhist forum that you might be ashamed of if your family and associates knew what you said? What would be the motivation behind adopting a Pāli name?