I need to know how each of these represent symbolism in Jane Eyre: Reed, Blanche, Gateswood, Lowood,Thornfield, and Whitcross.
Your question is a little confused and also seems to ask more than one question. Whilst you are right to identify that certain locations in the novel seem to have symbolic significance, the names of the locations you have given are not accurate. This answer then will point towards the 5 central locations of the novel and what symbolic significance they have in their naming.
Gateshead marks the first section of the novel, and the name certainly seems to indicate a feeling of entrapment or imprisonment, which is one of the key themes of the novel. From the very first sentence of the novel, where Jane is forced to stay indoors because of the weather, Jane is "gated" in, both literally, symbolically and figuratively, into a set role in society. Perhaps the "head" refers to the way that her being, her personality and thoughts are pressured to conform to this role as well.
The name "Lowood", which marks the next section of the novel, marks a "low" time in Jane's life, where she experiences suffering and the death of a close friend. It also marks her education and equipping for her "low" role in society.
"Thornfield" foreshadows the pain that Jane will suffer through her relationship with Mr. Rochester, indicating there is something that will spoil the supposedly happy ending that the text points towards.
"Moor House" and "Whitcross" both indicate the isolated position of Jane as she leaves Rochester and Thornfield, but also point towards a "resurrection" after the suffering of the "cross" that Jane has carried.
Lastly, "Ferndean" is a much softer and gentler name than Thornfield, indicating the happy ending that the text gives Jane and Rochester, and also perhaps suggesting the softening that Rochester has undergone through his experiences.
Bronte clearly divided her novel into 5 identifiable sections, and the naming of the locations are clearly indicative of what happens in each part, tracing the development of Jane Eyre as a character from start to finish.