While English law was applied to Wales about 1535 and there was strong encouragement to use surnames rather than patronymics, as you can imagine there was significant resistance among some who saw that as giving up Welsh culture.
The WikiTree ideal for LNABs is to "use the name they would have used." So IMHO, the earliest record for the person would govern; If he went by Gruffudd ap Rhys, ap Rhys would be the LNAB. If he went by Griffith Price, Price would be the LNAB.
It was an extended period of transition so different family members might be named differently. I think respecting the individuals themselves, and how they saw themselves, makes it necessary to accept a certain amount of messiness in naming, and to let go of our natural wish to see people with the same LNAB from one generation to the next!
Today, in an era of Welsh nationalism, you will see people identifying themselves by patronymics rather than English surnames. I know some countries like Iceland have very strict laws about what names can be given to newborn citizens; I don't know whether there are laws in the UK specifying naming patterns today. In the United States, it's pretty much "do whatever you want", although a family in New Jersey naming their child "Adolf Hitler [Jones]" lost their child to Child Protective Services several years ago.