Ros is partially correct - not every new project gets a badge that can be awarded, and there are restrictions on who can award the available badges.
However, if you are working with an existing project (and their Leader(s)) to create a Subproject or Team, you could be allowed to use that top-levels project's badge.
Help:Project FAQ has a short outline of the different types of projects, how they qualify for badges, etc.
If you have any questions, feel to reach out.