You don't need to stringify:
#include <stdio.h>
#define CHANNEL_ONE 1
#define UARTREG_(channel) UART##channel##REG
#define UART_REG(channel) UARTREG_(channel)
int main(void)
{
char UART1REG = 'a';
char UART2REG = 'b';
char UART3REG = 'c';
UART_REG(CHANNEL_ONE) = 'd';
printf("%c\n", UART_REG(CHANNEL_ONE));
return 0;
}