So... this is one of those questions where I'm hard pressed to answer exactly as asked, as the premise is somewhat leading. When a question is "Why don't I know about [X]?", "Why wasn't I taught about [Y]?", and so on, the answer is often less about an overarching narrative than it is about your specific circumstances and what you were exposed to. If you grew up in Alabama, I would expect that you are well aware of "Dixie", and if you grew up in Maryland, we can throw "Maryland, My Maryland" into the mix, but growing up in New England, if you asked me to play "song association" with the American Civil War, I would probably tell you "Battle Hymn of the Republic", a song I learned the lyrics to when I was quite young. I knew the words to Dixie too (I was a weird child! Don't judge me!), but that is somewhat beside the point.
I don't want to play 'which is more famous', as I'm not sure how easy it would be to measure that with precision here, but the point I do wish to make is that the North absolutely produced some recognizable songs. I would even be willing to make an argument that, while "Dixie" may have been propelled to immortality die to its association with the Confederacy, for which it served as an unofficial Anthem, it predates the CSA, while the abolitionist Julia Howe wrote "Battle Hymn" quite specifically in light of the war already commenced. Of course, Howe only wrote the lyrics, and she borrowed a tune from another song which is closely intertwined with the North, "John Brown's Body"", which was more popular with the soldiers of the time, even if we remember Howe's more somber and religiously infused lyrics today. "John Brown" was a much more organic song, as well, with lyrics varying from unit to unit, and it isn't even entirely clear to to credit with originating it. The melody is even older, and likewise in question, although ironically at least one possible origin of the arrangement is a South Carolinian, William Steffe.
Dixie is also ironic in that regard, since it was likely written by a northerner, Daniel Emmett, for a minstrel show put on in New York City in the late 1850s, although there is question as to whether he was influenced by tunes he heard from a free black family that liked in his Ohio town growing up. In any case, itss popularity with the Confederacy irked Emmett, who would be a staunch supporter of the Union during the conflict. In any case though, the only main point I am making here is that Dixie predated the Confederacy. It is up to you how that affects its standing as a "Civil War Song".
I would, however, bring up one more Northern tune I feel has endured, "When Johnny Comes Marching Home". Again, it comes down to a matter of exposure, but I think that it also stands as a tune which has survived to today, and as with Battle Hymn, it is both a song written during the war - not simply one which gained popularity during the time - and also likely not an original melody, as there is less clarity in the exact origin of the original tune here. "Johnny Fill Up the Bowl", with basically the same melody, was more popular during the war (just like with "John Brown's Body", but "Marching Home" - certainly a commonly heard tune during the conflict - weathered time better in the years beyond, and gained new popularity a few decades later during the Spanish-American War.
There are other songs which were popular, and you might find reference to here and there, such as "Marching Through Georgia", but I think it is fair to say that "Battle Hymn"/"John Brown" and "When Johnny Comes Marching Home" are the ones which endured best, and which are most likely known to modern audiences. I can't say why you haven't heard them - although perhaps you have and didn't realize their origins - so could only speculate it to be some combination of geography and interests, but I certainly don't think it is fair to say the North left us with no famous songs from the war.
Christian McWhirter's "Battle Hymns: The Power and Popularity of Music in the Civil War"
Steven H. Cornelius's "Music of the Civil War Era"