This wasn't just some random panel. It's the culmination of a sequence of events and the end of one of the phases of the arc.
Ever since escaping the tea party the straw hats were relentlessly chased through WCI. Each time BM got too close someone took charge and helped them escape the enemy. King Baum appearing. Pudding appearing. Nami using Zeus. Jinbe fighting Prometheus, and of course Pedro exploding. They were being narrowly saved chapter after chapter.
When they got to the ship and found Katakuri there, the plan was for Luffy to simply push him off and then continue on with them.
And that's exactly what Luffy was trying to do right up until Katakuri hurt Carrot.
It was only after Katakuri harmed Carrot that led to Luffy immediately dragging him into the mirro-world in order to prevent him from hurting anyone else.
After being relentlessly saved in the previous 10 chapters by other people, this was the moment in which Luffy himself took charge as the captain. This entire moment was meant to highlight Luffy's leadership and how he was entrusting his crew to hold their own, whilst they would then trust in him to beat Katakuri. This marked the end of the "return to the seducing woods" phase of the arc and was the climax of the volume.
That's why when Luffy calls Carrot's name out it is meaningful as this is Luffy properly acting as the straw hat captain and believing in his crew
including Carrot and taking measures to protect her and all the rest of them in direct response to what Katakuri just did to her.
To compare this moment to a scene that holds no weight at all for contrast, we can look at Luffy telling Yamao to protect Momo.
A small, messy panel with no build up since Luffy's essentially just telling Yamao to make herself useful. She's strong, and Momo's in danger so he told her to help him in addition to Shinobu. And of course he gets her name wrong which Oda has confirmed is because Luffy can't be bothered to remember what she's called.
As opposed to Carrot who he treats like one of his own and calls by her actual name.