EIN Change for Conversion from LLC (S Corp) to C Corp (S Corp)

Looking to convert single member Calif LLC (treated as S corp) to C / general stock corp (treated as S corp) using SOS conversion form.

***My question is whether it’s possible to avoid a new EIN for the entity?

 

Publication 1365 seems to say when incorporating an entity, need a new EIN.  Seems to apply here since going from single member LLC (disregarded from owner) to C corp.

 

But when I called IRS, agent said that since currently entity is an S corp, no need for EIN change; and can simply do a name change from LLC to Inc.

 

IRS agent said that because business name is line 1 of entity in IRS systems (and individual owner name is Line 2), they treat the entity as a corp (as opposed to business name being in second line and individual name in first line).

 

I have a feeling agent is wrong but want to get thoughts/suggestions/comments here.

 

Thanks in advance.