Traditionally they are called Dharma names.
When I became a member of the Rime Center, I was given the name Kalsang Dakpa, which means fame and fortune. When I joined the Five Mountain Zen Order, I was given the name Boepyol, which means Dharma Zeal. When I joined the International Ch’an Buddhist Institute I was given the name Heng Xue, which means Enduring Study.

What’s with all the fake names?

The practice originated, I think in monastic orders. If one became a monk and left the regular world behind, they would leave their old name behind too. It reinforced the fact that they weren’t a layman anymore, they were a monk now.

But now it’s used by the laity in a lot of places. I don’t know if the practice is as common in the east, but I suspect it isn’t. It is normal here to get a new dharma name every time you join a new community. It makes more sense for monastics because if you make the decision to become a monk in a certain order, you’re probably never leaving that order to join another one.

Why? To reinforce a sense of community, maybe? To make us feel like being a Buddhist has changed us, even though we haven’t given up everything to become monks?

I don’t know, but it’s something I am wondering. Also, are Dharma names helpful? I’m not sure. In some branches of Buddhism here in the west, they don’t use Dharma names at all. I wonder if collecting Dharma names is helpful.