If my mothers name she was born with is freydah but she is called chedvah by all then what is halchically her name/teffilot etc?
Answer:
If a name has been forgotten, and is not used in any context, it is no longer considered a "halachic name." The name she is called by (Chedvah) should therefore be used.
See Beis Shmuel 129:37, and in his names for gittin, under Sarah and under Ki.