Is there a word that describes a person who spreads others' secrets without their permission?
"gossiper" fits perfectly. (not specific for secrets, though)
- a person given to gossiping and divulging personal information about others - TFD
"yenta" is a slang word for a person, especially a woman, who is considered to be meddlesome or gossipy.
- a person who habitually reveals personal or sensational facts about others. e.g. "the couple's loud quarrel had the building's yentas yapping for a week." MW
related words: blab, gossip, gossipmonger, newsmonger, rumormonger, scandalmonger, tabby, talebearer, taleteller, tattle, tattler, tattletale, telltale, whisperer.
saying or doing things that tell people things that should be secret or that embarrass people:
In an indiscreet moment, the president let his genuine opinions be known.
They have been rather indiscreet about their affair. — cambridge.org
big mouth noun
a person who talks a lot, especially about himself or herself, and who cannot keep secrets
I'd use to describe someone who isn't deliberately leaking secrets. A bigmouth is usually someone who unthinkingly let out a secret.
Tattletale which means:
a child who tells a parent, teacher, etc., about something bad or wrong that another child has done : a child who tattles on another child
It is an old English adjective describing a person one would not trust with a secret - factual or false!
The other answers have some good ones. I just wanted to add
traitor to the list (at least, if they were let in on the secret and knew they weren't supposed to tell).
This also reminds me of the concept of doxing (if they weren't intentionally let in on the secrets). Doxxer appears to be in usage.
I would use
A person who habitually reveals personal or sensational facts about others