The incorrect spelling of your name may not be happening for the reason you think. I have a couple of cousins who have kids who’s name’s are common, but can be spelled differently (and I know several other people with the same name who actually do spell these names differently) and sometimes I forget. Examples: Carrie (Kerie) and Caitlin (Katelyn).
It seems like it might be more helpful for you to figure out why you often find yourself “not in good favor” with these 2 people. If the friend/acquaintence is someone that you know, but don’t particularly like, ease that person out of your life. If she is someone that you like, but often have arguments with, find out why. And then gently let her know that it makes you feel diminished if/when she spells your name incorrectly (she may not even know she is doing it for the reason I mentioned above).
And you really need to find out why your mother in law sees you as “not in good favor.” Do you argue often with her? If so, why and what about? You may need to get your husband involved in this situation. If MIL is purposely being rude to you for no good reason, then he needs to get her to stop. He should tell her that spelling your name wrong makes you feel diminished, since she’s known you long enough and you’ve reminded her often enough how to spell it correctly. But again, both of these people may not be slighting you on purpose (at least not with regards to the spelling of your name). If they are slighting you on purpose for some other reason, you need to get to the bottom of it and solve that problem.
My first and last names sound exactly how they are spelled, but you wouldn’t believe the number of times that I have to repeat and repeat and repeat how my name is spelled. And I sometimes get correspondence from people who have known me all my life who spell my name wrong. I have noticed that there are a lot of people who are bad spellers in the first place and there’s lots of people (myself included) who start typing too fast and accidentally spell common words incorrectly. And I am guilty as charged of sometimes spelling my relatives names incorrectly because I know other people who spell the same name differently. I mean no disrespect to any of them.