I try to create a struct, for example,

and then give it another name MY_STRUCT.
I tried
MY_STRUCT fix MY_STRUCTA,
MY_STRUCT = MY_STRUCTA,
MY_STRUCT equ MY_STRUCTA

and nothing works.
When using

mov [ebx+MY_STRUCT.param1], eax

after 'fix', fasm tells me "undefined symbol". What is wrong?

"struc{}" doesn't declare relative address labels (labels which give you address inside structure, like MY_STRUCT.param1).

For that reason there was created macro "struct" which does this at place of "ends". So these labels are declared here, and even if you fix MY_STRUCT later, there isn't any place where relative addresses could be declared with new name. Also "MY_STRUCT" in "MY_STRUCT.param1" isn't fixed because "MY_STRUCT.param1" is considered as single symbol to FASM. "." is part of name, not operator.