Thanks so much for your helps, I really appreciate the wealth of info@Edward_47
Disclaimer: I'm a student too. But I've bought 6 domains myself. And I've researched and learned advice and what business people think about when it comes to name, especially domain names. Also Matt Bailey talks about domain names in the Advanced SEO course.
Where to Buy Domains
You buy domains from a domain host provider. I don't really know what the technical name is, but examples are GoDaddy.com, ionos.com, and bluehost.com.
I think most website hosting platforms like Squarespace and other website hosting services can sell you domain names. There are so many businesses you can buy domains from. Bluehost is another one.
It's not very hard to find where to buy domains.
Most places I think you can buy a domain for about $10.
I'm not an expert, but as I understand, no matter where you buy a domain name you own it as long as you pay to renew it every year.
I use ionos.com because I like their introductory offers. I don't really know which is best to go with or the intricate details that differentiate different services. I've seen Bluehost recommended a lot.
What to Name Your Domain
First off you're limited to what's available. I think that everywhere you can buy a domain will all access the same available domains. It a domain is available, I think you can get it from everywhere. Premium domains are taken sometimes with the intention to sell for a premium price. But they're really expensive so I'd stick to available domains. There's plenty of available domains. I was surprised because I thought more would be taken, but there's still plenty of .com domains you can get, especially if you use made up words and hybrids between multiple words.
Domain name has a very small impact on SEO. Don't stress to get keywords in your domain. How I understand it, it matters so little as to be negligible. You can see this from the Advanced SEO course by Matt Bailey in our self learning content.
Make your domain type-able. You want for your domain name to be easily memorable and type-able. Recognizable words are nice, even if they have nothing to do with the topic of your website. You don't want an obnoxious name. You don't want a excessively long name.
Google your name before you buy it. It's so obvious, but I've been bitten because I didn't do this!
You want to see exactly how available the name is. The world's so big. There's probably some stuff out there related to or using the name.
I'm not a lawyer and I don't know all the legality about trademark.
I'm sure there's some circumstance where two ventures/project can have the same name. For example, if the name of your website is the same name as a foreign rock band and your website has literally nothing to do with. I assume in this case it isn't very risky to use the name.
There are probably instances where it would be trademark infringement. Like if another business is in your same nation and is actively using the name as their Doing Business As Name. In this circumstance, your probably don't want to use the same name another venture in your country is using.
Also, you don't want to use a name that is distasteful, illegal, or already as a negative meaning.
Make your domain name the same as your business name. You don't 100% have to. Like if your business already exists and you can't get that domain name. But I can remember Matt Bailey saying something about this. And think about it from a marketing standpoint. It makes a lot of sense to have your domain the same as your business.
Check social media that's important to you to see if usernames will be available. Check to see if you can get the same name for social media channels that are important to you. Or just similar usernames. It's up to you.
In conclusion, domain name (and business name in general) isn't going to be a make-it-break-it decision. The marketing behind the domain is what really matters.
Still, I think typeability (memorability & ease of saying/spelling), consistency (consistent name across Doing Business As name, domain name, and social media names), and availability are factors to consider.