If I want change postgresql encoding, I have understood that I should reinstall postgresql (I do installation from rpm official binary files for red hat)
I can't answer your question about whether the encodings need to be the same, but I'm pretty sure that's not true. CREATE DATABASE has options to set the encoding for a database:
CREATE DATABASE korean WITH ENCODING 'EUC_KR' LC_COLLATE='ko_KR.euckr' LC_CTYPE='ko_KR.euckr' TEMPLATE=template0;
To change the encoding of an existing PG database, you have to 1) dump it, 2) create a new, empty DB with the desired encoding, and 3) import the dump into the new DB. So you can't really change it "on the fly," but it can be done at creation time.
How it would be if I want latin9 encoding? I'm trying the next but it shows that it is not valid (es_ES.latin9):
