You can DM people on Mastodon by writing a post in "mentioned" visibility mode. In that mode, only accounts mentioned in the post can see it.

You can set post visibility by clicking on the visibility logo below the post:

🌎 - Public visibility, anyone can see it

🔓 - Unlisted, anyone can see it but not on main timelines

🔒 - Followers-only, your followers and anyone mentioned in the post can see it

@ - Mentions, only accounts mentioned can see it.

Find out more at https://fedi.tips/how-to-use-mastodon-and-the-fediverse-basic-tips/#WhoCanSeeMyPosts