He is also a Knight of the Order of Carl XIII.
It is not clear whether Julian has the Chain to the Order of the Seraphim but the entry for his christening on the Swedish Royal family's website is shown under his parents' joint monogram rather than one for himself. Carl Philip and Sofia's other sons as well as the children of Princess Madeleine and Christopher O'Neill appear to have had their monograms removed from the website, presumably because they no longer belong to the Royal House but the Royal Family.
We will presumably now not see another prince or princess of the Royal House until HRH Princess Estelle, Duchess of Östergötland begins a family. And we will see what happens with titles in the next generation when Carl Philip and Madeleine's children begin their families. Will they adopt a system similar to the United Kingdom where the great-grandchildren of a monarch become commoners?