We are in the same situation,our niece has been adopted by us in the UK and has a British passport in one name and her Thai passport in her original surname. Last year, when we were on holiday in Phetchabun we went to the amphur office to change her name to the British name. They would not do it and said that the only way a Thai can change their surname to a foreign name is by marrying a foreigner. They said that we had to get a stamp from the government adoption agency.
They suggested that we go to Bangkok to the government adoption centre and they could arrange things. (They really didn't know what they were talking about.) It was clear that we were asking for something that no one had asked for before. We phoned the adoption centre who said that we should turn up with our paperwork and they would make a decision in the fullness of time. They wouldn't tell us what paperwork was required, how long it would take or what their process for making the decision was. We explained that we were 400km away and on holiday and they still wouldn't tell us anything useful.
When we got back I contacted the UK passport office explaining our difficulties and they replied that they would consider having 2 passports in different names if we got a letter from the Thai embassy in London. We emailed them......and didn't get a reply.
Our niece's British passport runs out about a year before her Thai passport. We are thinking that we will have to let her be without a British passport until the Thai passport runs out and then get her a British passport because she will have only one passport then, so getting it won't be a problem. Then in the future at some time see what happens we she applies for another Thai passport.