Why is it that from one chapter to the next, people's names will change in Tower of God?
Name changes could be for a few different reasons. Most of the time, however, the English spelling differs because two different translators just decide to spell it differently.
In Korean, there is no Z sound. There is only a J sound, so words with the J sound like Jahad might be translated into Zahard depending on the translator's interpretation. As for the additional R in the name, that is really up for interpretation as well because English soft A sounds can be spelled like that. In this case, Zahard and Jahad will produce the same sound in Korean despite the English spelling differences. The spelling difference was only due to translator interpretations.
As for the Lahel to Rachel, this is a somewhat different case. Lahel is actually how the name sounds phonetically (pronounced lie-yell). Rachel is the English conversion of the name. It is like how the name Steven is Etienne in French. Lahel in Korean translates to Rachel in English.