All,
I am sure that the global financial institution, Chase, would be interested in taking legal actions against Chase Bank Kenya based on serious copyright and trade name violations. This is compounded by the fact the two institutions are in the same industry doing the same exact business i.e banking. What happens if Chase opens a branch in Kenya (like Citibank did)? It is like starting a search engine in Kenya and calling it “Google Kenya”, or starting bottling company and calling it “Coca Cola Kenya”, without having any affiliation with the real Google or the real Coca Cola company.

Chase Bank Kenya- Founded in 1995
http://www.chasebankkenya.co.ke/About-Us/History

Chase - Formed in 1955 by merger of Chase National Bank and Bank of the Manhattan company
https://www.chase.com/Chase.html

Lawyers will tell you that it's a challenge all over the world because you cannot copyright a word in the dictionary and that's why international companies avoid them. Just go to the registrar and you'll be shocked to find every company in the US has a Kenyan identical twin.

That reminds me...I need to register a trademark ASAP. What is the procedure and cost?

True it will be a long battle case like the one of Group 4 Security with G4S.
Anyway maybe Chase Bank Kenya strategy was Chase Global would come and buy them off/acquire them. Remember the idiot who registered safaricom.com and kencel.com domains hoping to sell the domains and make millions back in the days?

So, did he make the millions? Maybe not, you just called him an idiot....