Using one UK Ltd for freelance work and iOS apps?

Hello, need some help. I’m setting up a UK Ltd company for my freelance work in the creative industry - not related to app development.

I’m also building a few iOS apps. They may never make money, but I’d like to enrol in the Apple Developer Program as an organisation, so the App Store seller name is a company rather than my personal name. I’d also want to apply for the Small Business Program if eligible.

Since it just so happens I'm setting up the Ltd for freelance work anyway, should I/might as well use the same company for my Apple Developer account too?

If so, this means the name of my LTD company needs to somehow also reflect the apps I'm making (as that appears on the app store, right?)

Trying to kill two birds with one stone.

Then assuming, if an app takes off late (fingers crossed) can I set up a separate Ltd and move the app / developer account over to that new company? Or is it easier to just keep everything under the original company?

Trying to avoid setting up two companies before I know whether the apps will make any profit.

Has anyone done this?

thanks!