Changing Git remote URL updates fetch but not push

From git-remote manual:

set-url
    Changes URL remote points to. Sets first URL remote points to matching regex <oldurl> (first URL if no <oldurl> is given) to <newurl>. If <oldurl> doesn’t match any URL,
    error occurs and nothing is changed.

    With --push, push URLs are manipulated instead of fetch URLs.

So you should additionally execute:

git remote set-url --push origin ssh://user@example.com:XX/package/name.git