'Dogsong' is a prominent motif representing, uh, dogs, I guess.
Similar to some other leitmotifs in Undertale and Deltarune, 'Dogsong' commonly progresses from a standard variation, 'Dogsong A':
('Dogsong A' as heard in Dogsong)
To a slightly different variation, 'Dogsong B':
('Dogsong B' as heard in Dogsong)
While not expressly related to 'Dogsong', 'Dogroom' is a similarly dog-themed leitmotif that appears in relation to certain rooms of a particularly canid nature: