How do I rename a foreign key in mysql?

From the documentation:

Multiple ADD, ALTER, DROP, and CHANGE clauses are permitted in a
single ALTER TABLE statement, separated by commas. This is a MySQL
extension to standard SQL, which permits only one of each clause per
ALTER TABLE statement.

This way you can combine the drop and recreate into one query, and that should be faster than dropping the constraint and creating it in two queries:

ALTER TABLE conversation_tags
DROP FOREIGN KEY `conversation_tags_ibfk_1`,
ADD CONSTRAINT `fk_conversation_tags_tags` FOREIGN KEY (`tag_id`) REFERENCES `tags` (`id`);