You don't need to register a company unless you need to employ people yourself to get the work done. You can just register as self-employed. The details will vary depending on where you are. You'll most likely have to convince the tax authorities that it is genuine self-employment and not your employer dodging taxes. If you have an actual job with an employer abroad, you'll need to ask your local tax authority how to handle it.

Your hourly rate when self-employed should be around 2.5x the equivalent salaried hourly rate. This is because the employer is not paying for your admin time, training, equipment, office costs, holiday pay*, sick pay*, or contributing to your pension, or doing your taxes for you*. And because you don't have the security of a salary and will need to spend a lot of time bidding for work that might not pan out, while they get the benefit of having you on tap with no long-term commitment.

*these are not USian things but as a European you will still be losing them

It depends a bit on the field you work in but self-employment is not generally a great idea for a fresh graduate. Your degree qualifies you to become qualified and you can't easily do that on your own. Lack of experience will also make it hard to get the kind of work you need to develop your skills and get better work.