I am married to a Vietnamese Citizen does it mean we need to have the property on both names?

Yes, or no, depending on your ownership status of that property. In particular, Article 33 of the Law on Marriage No. 52/2014/QH13 dated on 19 June 2014 defines community property as all assets acquired during the marriage and are owned by both spouses equally. The land use right acquired after marriage is community property, unless the husband or wife acquire that property though heir ship or gift affidavit or separate transaction by his or her own property. In case there is no evidence to prove that one party individually owns a disputed asset, that asset shall be considered to be community asset.

Article 34 of the Law on Marriage 2014 provides that in case community property is subject to registration of ownership/use right, the certificate of ownership or use right has to be named by both husband and wife, unless both spouses agree otherwise.

Article 12 of the Decree 126/2014/ND-CP dated on 31 December 2014 of the Governmenton detailing and guiding some provisions of the Law on Marriage 2014 provides that property of a married couple shall be registered under both names. In case of separation of such registered community property during the marriage, one party can request the registration authority to reissue a certificate of ownership/use right base on the agreement between spouses or decision of the Court on separation of community property.

Source: AsiaReal