I am sorry to hear you are having difficulties.
I bet it is all even harder to deal with given your relationship situation.
Is the name change process where ever you live very cost prohibitive, especially given financial concerns for you at the moment? It may take awhile to process, but what about fee waivers assuming you qualify? Better to wait for the approval than do nothing at all.
In the meantime, take a deep breath and try to find the first step you can take towards doing something, anything at all, to help your situation. Consider how you present yourself at interviews and the clothes you wear, edit your resume, tailor cover letters for each job you apply for - etc etc.
There are always temp agencies. The employment agency screens you and then they look for jobs for you. It could take away some of the name confusion when they are doing the work to get you the job.