Cowrie shell at the bottom is the indexing radical. Cowries served as ancient currency, so 贝 marks 贺 as a wealth or gift word - congratulations were originally offered with valuable presents, hence its place beside 财, 贵 and 赠.
Sits on top and supplies the sound, drifting from jiā to hè along a regular Old Chinese pattern. The add meaning quietly reinforces the sense too: a congratulatory gift adds wealth and goodwill to the recipient.
