If it were me I would 1) do an UCC Search asap to determine whether any intervening liens pop up and 2) file a new UCC asap under the new name. I don't think it would matter if you filed a new one - or did a name change amendment on the old UCC to change the new name - after the 4 months has expired you'd be working off the new recording date of either. You might check with your legal counsel to make sure this is not different in your state as in what shows under Revised Article 9.
Below is an excerpt from Article 9 that details an amendment to change the name should take place within 4 months of the change:
EFFECT OF CERTAIN EVENTS ON EFFECTIVENESS OF FINANCING STATEMENT
(a) Disposition. A filed financing statement remains effective with respect to collateral that is sold, exchanged, leased, licensed, or otherwise disposed of and in which a security interest or agricultural lien continues, even if the secured party knows of or consents to the disposition.
(b) Information becoming seriously misleading. Except as otherwise provided in subsection (c) of this section and Section 9-508, a financing statement is not rendered ineffective if, after the financing statement is filed, the information provided in the financing statement becomes seriously misleading under Section 9-506.
(c) Change in debtor's name. If a debtor so changes its name that a filed financing statement becomes seriously misleading under Section 9-506:
(1) the financing statement is effective to perfect a security interest in collateral acquired by the debtor before, or within four (4) months after, the change; and
(2) the financing statement is not effective to perfect a security interest in collateral acquired by the debtor more than four (4) months after the change, unless an amendment to the financing statement which renders the financing statement not seriously misleading is filed within four (4) months after the change.
Just working here until I get my letter from Hogwarts.