Bees are opportunists - they'll use the pollen from whatever plant is closest to the hive first and only venture futher if they need to. This is why commercial growers can dump hives in the middle of clover fields (very common sight to see around here in the spring) and then call it 'clover' honey. While there may be other types of flowers in the mix, it will be predominantly clover.
For backyard beekeepers who are more interested in using their bees for pollinating gardens and orchards, it's helpful to NOT plant bee-specific flowers in the immediate area of the hives so that the bees get used to traveling futher afield for their pollen. Our bee flowers are planted near the edges of our property and the bees are located directly in the middle of our orchard with the garden between them and the wild flowers, all intentionally.
My guess is that you can probably label honey by the type of flower even if you are not a commercial grower depending on where you live. If you live in an area that really only has clover blooming from x date to x date and you harvest honey before the next main type of crop goes into bloom - then I would think you could safely call it 'clover' honey. I don't know the actual rules about this though.
I should also mention that 'local' honey is different from 'backyard' honey. Local honey can be produced by growers who do transport hives - they just do it locally. Sometimes they contract with berry farms or grass farmers and sometimes the berry farms themselves have bee colonies to move from field to field. Backyard honey comes from hives that don't get moved. These hives would only produce 'clover' honey (for example) if that person's backyard happend to be on the edge of a clover field with nothing else growing nearby. Most backyard producers due use seasons to differentiate their honey. Though, for us, near the mid to end of the summer, the only thing that is still blooming are the blackberries and I suppose that if we were in it for the 'types' of honey, we could make that work. We don't because our abilty to harvest honey is only the secondary reason for having the bees. The bees get first dibs - we only harvest in late spring when the bees need less of it. We'd never pull it out of the hive in the fall.

