How important is the name of a trust?
Actually, it is of no importance at all. It is the IT number that distinguishes one trust from another. So, unlike companies, there can be numerous trusts with the same name, but none with the same IT number.
But, please be kind to whoever keeps trust documents on file. Do not make “The” a part of the trust’s name. It’s much more difficult to find “The Charlie Family Trust” amongst a whole load of other “The” entities, than it is to find the “Charlie Family Trust”.