I used to omit my "unused" first name from flight bookings, and rarely had problems, even on long-haul flights.
While I don't think it is technically necessary to have all your names on the flight ticket, some airlines may reserve the right to deny boarding if your id doesn't match you ticket. At the end, this will often come down to the individual agent.
I had problems once or twice when I got extra scrutinity (e.g. because I travelled on a one-way ticket), so I put both names now just to be sure.
Unfortunately, your experience may also depend on your country of origin, depending on how "well received" the nation is at your destination.
That said, I wouldn't be particularly worried if you're from a western European visa-exempt country.
If you want to be on the safe side call the airline and ask if they'd allow you to board. Many airlines will even straighten out honest mistakes without a fee. If there's a huge fee involved I'd probably take my chances.
In any case I'd always put my full names for everything to do with immigration.
While this doesn't include the name on the ticket, it does include the passenger data that you submit through the airline (together with you passport number and other personal details). This data is usually entered in a separate step, but it's up to the airline's system if you can put a different name there.