While creating a client you will notice that there is an option to put a "Secondary name".
Let's assume that you are working with a client named "WaterWays LLC". You sent an invoice to "WaterWays LLC" and you got paid via direct deposit to the bank account. Later when you look at your bank statements then you will see many deposits and one of the deposits has the name "Modern Reality Inc". You had never heard of this name. After some effort, you found that the deposit from "Modern Reality Inc" is a deposit from "WaterWays LLC".
In such cases, you should put "Modern Reality Inc" as the "secondary name" of the client. Once you do that then if you go to the search panel of Invoices tab and there if you put client name as "Modern" then the result will contain "WaterWays LLC". That's because when you want to search for a client named "Modern" then the application will search for both the primary name and the secondary name of the client.