I've noticed a resemblance in tribe names. I know that the Kingdom of Kush and the Kushan Empire are divided not only by a substantial distance but also a substantial amount of time. Is there any reason to believe that there is a relationship between two tribes?
No, there isn't. What you have here is a coincidence. There are only so many sounds that the human voice finds easy to use in language, so similar names come up in different language groups.
Language groups also reveal the lack of connection between the two "Kush" groups. The Kingdom of Kush was Nubian, speaking Afro-Asiatic and Nilo-Saharan languages. The Kushan Empire spoke Indo-European languages. This is strong evidence against an ethnic connection, which the distance in both space and time made very implausible to start with.