Yes, you can move your account from one Mastodon server to another, and it lets you transfer your followers, follows, bookmarks, lists, mutes, blocks and server blocks.
Click here for an easy-to-understand step-by-step guide to the entire account transfer process ⧉. This guide also answers lots of questions about transferring your account.
Will my follows and followers transfer too?
Yes, if you follow the process in the guide they will automatically transfer to your new account.
What about my posts?
They stay behind on the old server, but if you follow the guide they will redirect people to your new account.