I understand that you need to see the entire product name when searching on the invoice. Let me assist you!
The most possible reason why it's not showing the entire product name is that your screen resolution isn't compatible. You'll want to set it to 1024x768 or higher and make sure that the Dots-per-inch (DPI) is set to "Normal" or "100%".
In addition, you'll want to check and see if the page is zoomed in. You'll want to zoom it out so you can see the entire page as well as the entire product name. Simple hold down the Ctrl and the minus (-) keys on your keyboard.
If the same thing happens, you'll want to use an incognito window and check the invoice from there. Incognito won't save your browsing history which can result in an error. These are some of the shortcut keys:
Did you receive the client's payment? Here's the article on how to record it in QuickBooks Online: Record invoice payments in QuickBooks Online.
Comment below if you have other invoice-related concerns. Take care!