Can my spouse buy a HDB under her own name only

No, if the seller's spouse is not a co-owner/occupier of the flat, the spouse needs to endorse the Resale Application Form. The spouse must attend the first appointment and sign the Spouse Consent To Resale form in the presence of HDB's Resale Officer. If the spouse is not in Singapore or residing overseas, HDB will require the spouse to sign the form in the presence of a Notary Public.