Per IRS Publication 1635, a new EIN will not be needed where "after a corporate reorganization, you only change identity, form, or place of organization." (Pg. 4) "Corporate reorganization" includes when an entity converts.
In order to update the EIN information with the IRS you'll need to send a letter to the entity division as follows:
Mail to:
Internal Revenue Service
Stop 6273
Ogden, Utah 84201
Heading of letter:
EIN number
Identify person sending the letter and relationship to business.
business name
business address
Body of letter:
State specifically what changes need to be made. In this case, update the business name.
Attach:
Art. of Incorporation filed with the Cal. SOS.
Recommendation:
It will take an estimated 30 days, maybe longer, for the IRS to process this change. We'll need to convert with the California Secretary of State first and then make the changes with the IRS. I think this justifies that we get started with the State filings sooner than the end of the quarter to prevent any major hold with the banks.