I hereby submit the answer
The small estate affidavit allows entitlement to a person to receive the possession of the property held with the deceased (i.e. in your case spouse). It is without formality of the probate. In the affidavit, the individual must identify any other claimants too (ff any). The Affidavit must be signed and sworn before the notary of the state where it is going to be filed.
Is it necessary to have the account name and SS# XXXXX to your name in order to closed it out if you already have filled out a small estate affidavit
The person who is the legal heir of the deceased should submit such affidavit and should give the details of the account name and SS of the entitled person.
When already filed the Small estate affidavit, no further details required
The question remains. Must you, as the new recipient, have the deceased's account changed into your name if the small estate affidavit has been properly filled?
Please note that the recipient who is legal heir of the deceased should submit small estate affidavit giving his/her details of account name and SS. For example if wife has died without will, the husband can submit small estate affidavit.
Is the small estate affidavit just for the purpose of giving needed information or for by passing legal changes in the formentioned account
It is without formality of the probate. The legal changes are to be effective by giving such affidavit