I have two given names and one surname. Is it a problem if I omit the surname from my ticket?

I have two names as my given name in the passport and I typically just use this as my first and last name. However, my passport has a surname too which I almost never use. Due to this, I mistakenly provided my given name as first and last name.

As per the passport, Surname : AAAA Given name(s) : BBBB CCCC

In the ticket, First name : BBBB Last name : CCCC

The credit card I've used to make this booking has my name as BBBB CCCC.

Will this create a problem at the travel time?

Update : the airline says that they can't update the name in the ticket. They are saying that since they have made a remark of the passport details boarding will not be a problem but I might face problems at immigration. Do they check name details in itenerary to exactly match passport at the time of immigration? Is that true in your experience?

Update : Travelled without any problem, neither at boarding gate, immigration nor after arrival at border police control.