Adding "SWA" to a parking position in airport customization did not change the logos.
And that's exactly how it works. Those codes are only a "booster" in the scoring process, when there are multiple operators with the same score as candidates, the code there will act as tie-breaker to select one, but possibly more than one, if there are still more than one at the same score, after getting the score boost due to the matching code.
I was also expecting an option to pick an operator.
Of course there is one, the two lists, one for catering and one for handling. Those will take precedence over anything, so you can set any operator or any airport/parking, regardless of the rules and the scoring.