You can buy more I Bonds at TreasuryDirect in a trust. The trust can have the same tax ID, email address, and bank account as your personal account.
You can set up a beneficiary or a second owner on your I Bonds in TreasuryDirect. It only depends on if you want to let someone transact on your behalf.
If you own savings bonds with a second owner in TreasuryDirect, you have to specifically grant rights for the second owner to see or redeem the bonds.