I have a feeling like I might have asked something along these lines before but my wife and I have a little issue here.

Our youngest daughter's name in Alicia, pronounced "Ah-lee-see-ah". My wife's Aunt and Grandmother have both in the past announced to us that they "don't really like that name" and planned to call her "Ally". We kind of brushed it off or just reiterated that her name was Alicia.

Now Alicia is 1.5yrs old and is at that age where she is starting to talk and understand when we talk to her. I feel bad because now when we go to family functions there is 2-3 people calling her Ally, to which she doesn't respond too at all(why would she) and they get angry that she doesn't pay any attention to them.

We've made it clear we don't care for "Ally" at all and she doesn't respond to it. What else would you guys do??

I would just tell them if they expect her to listen they need to use her name. Or be a total ***** and make up some name for them and call them that all day long to see how they like it.

I agree. I would just remind them that she responds to Alicia. Good luck!

They are being stupid.
 
I like Savanah's idea to make up a nickname and call them that.

My sister & dad have always insisted on called Leanna "Lea" but she didn't have a problem responding to the name even though she doesn't like it. She has recently started standing up for herself and telling them that her name isn't Lea.

Yeah, I wouldn't do anything about it, except maybe say, "if you really want her to pay attention, just use her name," or "is there someone here named Ally? Can I meet her?"
Plus, honestly if they spent enough time with her, she would know that they're talking about her already. We call Brady all sorts of names "Big B., Bray-Bray, Bradyman," and he answers to all of them, because he's used to them.
In that situation though, I'd do nothing. Either they'll learn to use her name, or she'll learn to respond to Ally. Eventually, she'll correct them, embrace the nickname, or go by something totally different.