That's a good question, actually. I don't know of any definitive answer, but I can guess on a few reasons.
1. Over at TestOutfit, we were occasional prone to naming our squads "Test Squad Best Squad" and the like. This may have transitioned over to Test Squadron Best Squadron.
2. To more easily differentiate between us and TEST EVE, who are "Test Alliance Please Ignore"
3."Test Squadron Best Squadron" fits better on the logo than "Please Ignore"
4."Test Squadron Best Squadron" is closer to rhyming.
5. I think we're actually still Test Squadron Please Ignore, but "Test Squadron Best Squadron" is a catchphrase sort of thing.
If someone's going to elaborate on this, can you do it in a different thread? Just to prevent colossal tangents.