A customer wants to open an estate account in the name of a e.g. The Estate of John Doe . That's how the Estate documents read; however, the SS4 form from IRS reads, John Doe Estate. We are styling the account as the legal document reads which is The Estate of John Doe and making sure the IRS code is correct.
Does it really matter that they are not identical in this case?

No, it does not make a lot of difference beyond the fact that "The" is superfluous.

If there is information reporting involved, the IRS computer is capable of reading the first two 40 character lines of the account title. Keyed by the EIN, the computer is searching for DOE. Whether it's the second or the fourth word, it will stop when it finds it and call it a match.

Regardless, your employees should have a style sheet that tells them how all accounts recognized by the law in your state says they should be titled. (Customer opinions will not be sought.) Although it makes little difference, putting the name that goes with the TIN as early in the account title as possible just maximizes your chances of a match; e.g. John Doe Estate, by Jane Brown, Personal Representative.