I was shocked that there were people confidently telling me my documents were wrong when I knew for a fact that they hadn't a clue what the law was. If it's part of your job to deal with name changes then I expect them to be trained on the subject.
The bank had its own internal definitions of what a deed poll needed to be - a definition they didn't publish anywhere and then act like I was the daft one for not knowing the specifics of their fanfic legal definitions.
Deed poll was sufficient for both of those for a name change for me, as well as for the registry office two months ago. I cannot speak for changing gender though, merely name.
Lots of places are very weird about it though because their staff think we have "legal names". I switched banks over the weird bullshit mine was pulling. The number of looks my piece of A4 with a couple of signatures on it has received from staff that then have to go check with someone that it's actually how it works, my gods. No, I know it doesn't look fancy, it doesn't have to, go ask your supervisor if you don't believe me.
In the UK you can. We don't have a concept of legal names. We do have far too many TERFs and other nutters though, so...
That's some very sedate drum and bass.
Land of the free, everyone.