String.prototype.replace only replaces the first occurrence found in the string. If there could be more than one occurrence, use String.prototype.replaceAll which is new-ish as of ES2021.

const petName = 'Leo'
const placeholder = '{NAME}'
const reminderTemplate = '{NAME} is due for another visit. Please call us so we can set up a new appointment. We look forward to seeing you and {NAME} soon.'

const reminder = reminderTemplate.replaceAll(placeholder, petName)