From https://drafts.csswg.org/cssom/#dom-window-getcomputedstyle, the signature is
getComputedStyle(elt, pseudoElt)
where pseudoElt is parsed as a <pseudo-element-selector>.
For example, ::before or ::marker are <pseudo-element-selector>s.
However, https://drafts.csswg.org/css-pseudo-4/#marker-pseudo allows ::before::marker and ::after::marker in stylesheets. These are not a single <pseudo-element-selector>, but it seems useful for authors to expose their styles via getComputedStyle.
So maybe we could allow one of these:
getComputedStyle(elt, "::before::marker")
getComputedStyle(elt, "::before", "::marker")