Yes, you can - and you can switch between users, too. Once you're signed in, you can add other users by clicking on the Sign In icon at the top of the screen and selecting 'Add new user'. That's also how you can switch between users.
If you've got multiple people signed in on your device, BBC iPlayer will ask you to 'Select who's watching' when you launch the app.
How will I know who is signed in on my TV?
Each time you launch the app the signed in user’s display name will appear in a tooltip next to the Sign In icon.
What is the Guest Account?
If someone else wants to use BBC iPlayer on your TV, you can use the Guest Account. The 'Guest' option will appear when you launch the app, or you can switch to it by clicking on the Sign In icon at the top of the screen and then selecting 'Guest'.