Remove project from my Google Cloud account

Here I guess you hold an Editor position within the project.

[UPDATE] Only the owner can delete the project. However other primitive-lower-level roles can ask the owner to remove their access. [/UPDATE]

if you are not the owner of the project, you can't get removed at once. Please ask your previous company to remove your access permission to this project. As I know so far, Lower-level roles(even Editors) cannot leave the project without any action from the owner.

And refer this to learn about user roles in a Google Cloud Project.

Google's Cloud IAM feature manages all the access levels as specified by the project owner or high-level roles.