Can you get email on your own domain with your hosting?
With most regular hosting plans, email on your own domain is included. Note: specialized WordPress hosts like Kinsta and WP Engine deliberately do not host email; there you arrange mail separately, for example through Google Workspace or Microsoft 365.
An email address on your own domain looks professional and comes standard with traditional hosting plans: you create mailboxes in the control panel and read mail via webmail or your own mail app. Hostinger, Namecheap, DreamHost, IONOS, and A2 Hosting all include it with their web hosting.
The exceptions are the specialized platforms. Managed WordPress hosts (Kinsta, WP Engine) and cloud providers (DigitalOcean, Hetzner) deliberately do not run mailboxes; running email well is a discipline of its own. There you connect an external mail service to your domain, like Google Workspace or Microsoft 365, from a few dollars per user per month.
Honest advice: for business use, such an external mail service is worth considering even when your hosting includes mail. Deliverability, spam filtering, and storage are in a different league than bundled hosting mail, and your email never has to move again when you switch hosts.