Yes, a newly created Living Trust can be named the same as a previous Trust.
But the name of the old trust and the new trust will likely be dated differently, which can require the transfer of assets as well.
If the old trust had a specific date within its name (e.g. ‘The Smith Family Trust Dated March 1, 2000’) and you funded the trust under that specific name so that real property is now held in the name of the “The Smith Family Trust Dated March 1, 2000”, then you may need to transfer assets to fund the new trust.
To easily create new Trust documents, see Standard Legal’s Living Trust legal forms software.