Any income received by foreigners outside of Thailand is exempt and not subject to Thai tax, unless it is remitted to Thailand. Any income remitted to a Thai bank by a foreigner is now subject to tax.
As I've tried to explain (yes, as I would to a 5 year old), those US accounts needn't be the issue. She can open an account in Thailand and transfer the money into it. We are in a THAILAND advice group after all!
You have obviously been going to the wrong banks or the wrong branches - I have opened 4 accounts at different Thai banks over the years, using only my passport. Remember, many countries don't have "State IDs" in addition to passports. You appear determined to make things much more difficult than they should be.
Like far too many Americans, you seem to see everything from a very insular point of view. The whole world is not the USA. She can open a bank account in Thailand or elsewhere using her passport as identification, as many, many others have done.
Whether a woman's "married name" is her legal name depends on the jurisdiction. Marriage does not automatically change a woman's legal name, and a passport can only be obtained in a person's "legal" name.
I have lived in Thailand for more than 30 years and maintained my Westpac account in Australia (yes, I informed them of my Thai address). You shouldn't have any problems.