A good garden designer should be able to suggest a rough idea of what level of spend you should consider based on their initial discussion with you, as long as you have been able to provide a good level of detail of your essential requirements.
Having a ball park budget in mind is always a good starting point but be realistic about the possibilities if your budget is limited. Often people are reluctant to disclose to the garden designer, the budget they have available or as is just as often the case they have no idea of what they want or need to spend.
Disclosing the budget to the designer from the outset, does not influence the design fee. The design fee is more often than not based on your garden size or on larger projects, a percentage of the build cost so there is no earthly reason to hold back this vital detail.
Letting your garden designer know how much you have to spend, makes it altogether more likely that the commissioned design work will actually come into being and not just a concept on paper.
There is little point in spending time and money getting a beautiful garden space designed if the construction budget is not there for it.
Here is an article in the Daily Telegraph giving an insight into the potential costs involved in designing and building a garden.