This is a follow-on post from an earlier one about names, here - I've recently made some clarifications around this stuff, and I wanted to make sure I'm not setting anyone on the wrong track. In short, just about all of what I said last time still holds, but there are a couple of additional wrinkles to be aware of.
First up, contrary to what I said previously, the two bachelor names of the marriage can be combined, either with hyphenation or a space, and hence Rose Smith marrying Greg Jones could become Rose Smith-Jones, and that would be generally recognised. Furthermore, if one of the bachelor names is already a hyphenated name, there's no rule against combining that with a third name (although there comes a point where you want to think very carefully about whether you're going to be making life unnecessarily difficult for yourself...).
But there is a bigger point to make here, which is that a change of name as a result of marriage is what is known as an assumed name, and is different than a legal name. If Rose Smith marries Greg Jones and takes his surname, she is still legally Rose Smith, but may go by Rose Jones as an assumed name.
You can see more info about these rules on the government website here.