The server announces the score before serving.

Rule 4.K.
If the server announces an incorrect score, other players can legally stop play for correction before the serving team hits the "third shot."

(1-Serve, 2-Return, 3-3rd shot.)

This is how this is handled at tournaments. It's more informal at club-level.

Correcting the score during play is a distraction.

This messy situation can be avoided:
• Server announces the score
• Server pauses for 1 second (opportunity for correction)
• Server serves.