A few have mentioned calling out who is on deck each turn, and this does help.
I also break up every round into a declare and act phase. At the start of each round, I ask the players what their intentions are in broad terms: melee, ranged, spell, other. They may, but are not required to declare a specifc spell or target. They can also ask questions or coordinate. Then I go through everyone's turns. While I'm talking to the current player, everyone else is allowed to looking things up and make rolls in advance. The effect is that players spend most of each round engaged and active, and individual turns also go faster.
In my most recent game, I stopped using individual initiative, and started relying on their declared actions to determine turn order. All ranged combatants go (including ranged cantrips). Then melee combatants. Then spellcasters. This gives the most complex actions the most preparation time and makes everyone aware of roughly who's going when. This allows for others to respond to the possibility of a big spell, or to effectively delay their actions to the right moment. For example, a ranged fighter might say, "I hold my fire until the orc is on the bridge", or the barbarian can say, "I attempt to choke hold the enemy wizard to prevent their spell".
I only call for an initiative roll at the exact moment it becomes necessary. If there are multiple sides acting in the ranged phase, I might call for a group initiative roll. If two melee combatants are facing each other, I have them each roll initiative to see who strikes first. Same with spellcasters, as the order of spell effects often matter.
Doing it this way, we fell into a rather natural cadence. The goal is to keep the energy high, keep the PCs thinking like a group, and reduce the board-game-like nature of D&D combat.