The groups listed here can provide some legal support in transition and may be able to connect you to further resources. Some may run name change clinics that would support a transgender person through the whole name change process while others may be more informal.
see the citations pdfs for relevant laws in each state
A state by state guide to birth certificate changes in the United States
Political lobbying and educational organisation campaigning for equality and human rights for British trans people through legislation and social change. The original website is archived here.
US-based organisation seeking to raise the voices of marginalised trans people.