As of my knowledge cutoff in September 2021, most mattress manufacturers do not offer custom heights, as they typically stick to standard sizes to accommodate the majority of consumers. However, there are specialty mattress manufacturers who may offer customization services, but this often comes at a premium cost. (Nine Clouds Beds offers custom widths and lengths but not height)
Customization can include not just the size of the mattress (length and width) but also the height or thickness. These custom manufacturers might make a mattress that's thinner or thicker than standard sizes, depending on your specific needs. (If you choose a custom height it's crucial to understand that your mattress will never feel the same as the one you try in a showroom)
However, bear in mind that a mattress that's too thin might not provide sufficient comfort or support, and one that's too thick might be hard to get into or out of, or might not fit standard sheets or bed frames.
It's important to research and communicate clearly with the manufacturer to ensure you get what you want, and it's also a good idea to understand the implications in terms of cost, lead time, and return policy for custom orders. (No one offers reselections or returns on custom size mattresses)
You can also consider other options to adjust the height of your bed, such as using a mattress topper (not a great solution ) to add height, or adjusting the height of your bed frame or box spring (good solution)
Please note that the information might have changed after 2021, and it is always best to check the current state of affairs.