It's not so much changing vitamins but rather changing the nourishment that your body NEEDS that can affect your growth. You could take the same vitamins without changing them till the cows come home but if you're not getting the nutrients that your body needs for all your cells to be happy, then your hair will not get the nourishment it needs and so you will not see any positive progress in your hair.
Changing your vitamins from one that was not providing your body with what it needs to one that does would make your hair grow better, so in that case, changing vitamins would be a good thing.
How do you know what your hair needs? It's really hard to say, which is why my rule of thumb is to get a good multi and eat well and stop worrying so much about jumping on bandwagons. If you were taking biotin but also eating foods high in biotin, the extra biotin would be peed away or you'd break out and you'd wonder why you don't see any progress in your hair. It's because you aren't deficient in biotin but might be deficient in something else like sulphur/sulfur. Maybe MSM is what you need. Maybe iron is what you need. Maybe vitamin A is what you need. See what I mean? Better to take a complete multi and even an enzyme if you suspect your body isn't breaking it down properly.
Sometimes it may just be that you're already at your optimum growth rate so nothing extra you do will make a difference. Sometimes it could be that you have some deficiency that could be caught in a medical exam that could point to what particular supplement you need to maximize to healthy hair.
