In the US, kyu grades they are typically issued by the national organization only. However, my understanding is that a student who requests it can also have the grade registered through Hombu. This would seem to be what it is meant by Article 11 of the Hombu International Regulations
, which states that "All practitioners of Aikido must become members of the Hombu at the time of the registration of the 1st dan grade or earlier
. [emphasis added]"
I beleive that registering a kyu rank with Hombu also entitles one to a "yukyusha book," the kyu grade equivalent of the Hombu yudansha book. Of course, you should contact your national organziation if you have any questions on its specific policies.