In ordinary daily-life Japanese at the moment,
メリー only means a person's name 'Mary' or 'Merry'. And even for 'Mary', it is usually written as
メリー is seen only in a few established expressions like
メリーさんの羊 'Mary's little lamb',
メリーポピンズ 'Mary Poppins', or
クイーンメリー 2 'Queen Mary 2'. Also 'Merry' is not much popular name, and is limited as in
メリー喜多川 'Merry Kitagawa'. Other than that,
メリー cannot be seen as a word in ordinary daily-life Japanese.
メリークリスマス is a gairaigo (crucially, not wasei-eigo) that originated from
Merry Christmas, which means that you cannot divide
メリークリスマス into its parts and make sense. The original English expression
Merry Christmas can be divided into
Christmas, but dividing the Japanese word
クリスマス is no different from dividing it into
リークリスマス; it does not make sense, and these parts do not have any terms by which they are referred to.
クリスマス is another gairaigo that originated from