I've been practicing 3D modelling for a few months now. I want to find a way to sell models, maybe make models on commission. However, at least at the beginning I don't want to do this using my real name / let people see my personal info. Are there any sites or ways where I can do this? I mean where the site can see my personal info but doesn't share it with people who buy the models, so handles selling / payment indirectly.
Websites like Fiverr.com allow you to do freelance work relatively anonymously. As a matter of fact, it's against Fiverr's policy to share your personal information on the platform. Working this way would be more like if someone asks for something specific and you create it custom for them, as opposed to having a stock built up and just sell them passively like on shutterstock.
There is, of course, the option to create your own website that allows users to purchase downloads. I used BigCommerce.com last year to open a store and BigCommerce handles all of the payments for you where the seller and the buyer never directly share information. While your profits will be much higher on a platform like that, all of the advertisement will be up to you, since you are pretty much running your own business. On Fiverr, you are part of a community and that can help you get noticed much more easily.
You can look at sites like TurboSquid, CGTrader, 3DOcean, Evermotion, CreativeMarket or even Adobe's 3D assets store for its proprietary 3D tools... all of them use a similar modality to those stock sites already mentioned - though most of the previous ones mentioned were image based versus model based (which these all are).
If you have enough skill and proficiency, you might also be able to sell assets for specific game engines in each of those asset stores, as many independent games developers are not hotshot modelers themselves - I know the Unity Asset Store has a slew of 3d assets from free through quite expensive, and from barely passable quality through to better than I could produce myself; I would imagine the same to be true for Unreal as well.
OH - hey yeah - if you ARE really good and you excel at high clarity, good edge flow poly and Sub-D modeling and can do excellent quality architectural and environment assets, you could see about submitting models to Kitbash 3D - they do top-flight work, work with only excellent modelers, and they do specifically commission thematic work from those modelers - they charge real money for excellent quality assets, and the artist get paid pretty well.