How can I assign the tasks to someone, team or me without sharing the project? It will be perfect if we can input the someone or team, like: projects
Unfortunately, this is not currently doable right now. You need to share the projects before you can assign tasks to someone. You can, however, suggest a feature request in the votebox https://todoist.com/Vote/. This is one way to determine which feature requests are popular among other Todoist users.
Please let me know if you have further questions.