I have the same situation, though my suffix is less common. My strategy is to drop the suffix when purchasing a ticket, which has mixed results. Some airlines

I have the same situation, though my suffix is less common. My strategy is to drop the suffix when purchasing a ticket, which has mixed results. Some airlines (United) remove the space between my last name and suffix when I do have to use it (International flights) which caused me some angst until I figured it out.