Rooting your phone allows you to install software that you otherwise wouldn't be able to, due to carrier or device software limitations.
IF you root your phone, there are a large number of hotspot apps that you can install that will provide a hotspot for you. ROM's are usually just a collection of software (with the occasional performance tweak) that you can install. 99 times out of 100, ROM authors have merely borrowed someone else's hotspot app and packaged it in with the rest of the apps that they like. So no, you do not need to install a ROM just to install a hotspot app.
<Necessary Legalese> Keep in mind though, that if you cannot install a hotspot app and one was not provided on your phone, it's likely against the terms of service from your carrier.