If you are a new PI you can absolutely deposit plasmids you made during your postdoc. These plasmids however need to be deposited under your previous PI’s name and institution. The institution the construct was made in and the PI of this lab is necessary to effectively process the Materials Transfer Agreement.
These plasmids however, can also be listed under your name on Addgene’s website. To complete these types of deposits please email email@example.com with your previous PI’s written permission and a request for your name to be added to the deposit. Written permission simply consists of an email confirmation from your previous PI with his/her willingness for you to deposit the plasmid/s with Addgene on their behalf, and to have you listed as a depositing lab on the plasmid pages. Be sure to include the deposit number (assigned after deposit submission) in the email.
Once you have been associated with the deposit your name will appear on the public plasmid pages as a depositing lab adjacent to your postdoc advisors name. These plasmids will also appear on your Addgene PI page along with any other plasmids you deposit moving forward.
Please note that rewards points are only eligible for the PI/lab and institution that first created the plasmids. So for the plasmids created in your postdoc lab, your new lab will not be eligible to use these points. You will start to accumulate your own rewards points once you initiate your first deposit from your new institution.