I have been searching for the meaning of the pseudonym Eui-Am. I know the definition, but what does it mean. This is the most I can find "The Taekwondo pattern Eui-Am was named in honor of Son Byong-Hi after his respectful title of Eui-am Seong-sa". But I am unable to find more.
When joining a religious movement or sect in certain east Asian cultures it is common for acolytes to receive a new religious name. 의암 ("Eui-Am", lit. "Righteous Rock") appears to have been such a name given to Son Byong-Hi when he joined the Donghak movement, either when he was initiated or possibly when he was ordained as the 3rd Great Leader in 1897.
He appears to have maintained and was commonly known by this pseudonym during his years in the Korean independence movement.
According to this link, "seong-sa" breaks down into "sage" (seong) and "teacher" (sa). Although it's usually translated as a "grandmaster":
And according to everything else I've read, it appears that "Eui-Am" is just a pen name to conceal his true identity. It probably means something, but I can't tell what.
Hope that helps.