Hello. In order to host your website on Railway, you will need the Hobby plan which is 5$ per month. If you've qualified for the free trial, you also have the option of the serverless free plan, which is less performant but is likely fine for a simple website.

You can change the project name through the project settings. After clicking into the project on the dashboard, click the settings button at the top right.

I already have exhausted the free plan , used to for the deployment of my discord bot , and now its exhausted.

Actually my website is not simple i guess, im gonna explain its functionality , to make sure if the hobby plan can do the job perfectly for me..

Its a platform where i will showcase all my discord bots , android apps , games (max size 500MB to 1GB , for now <100MB) , users can download the APK files for my showcased apps , and exe file for the games , users can also also order android apps , discord bots for themselves.
Also there will be a place for creating free discord bots for anyone on the website itself , no coding skills will be needed for that , they will be naming the commands and stuffs that are asked on the webpage and based on it the code will be generated for them.

That's all... so is hobby plan gonna do the job ?

I also have a domain name bought for my website , can i use that domain name after i host it from here?

If you've been using the free plan successfully, then Hobby plan will work for you. There is little difference in the offerings between the two aside from resource limits.

Yes, you can use your domain name for your Railway app. Docs