You should reset all client related cache or storage variables on client_connect or client_disconnect. Caching the players name is not necessary unless you use it in a very frequently called function (such as Client_PreThink). Cache steamids on client_authorized and you will be fine.
Please post the problematic code here or create a small substitute plugin that exhibits the same issues. It is much more helpful if we can solve this problem in the public space so others (like bol) can find the solution.