Contact form spam is very common, and the best course of action depends on what's powering your contact form.
Note: We always recommend having your email address on display even if you're encouraging people to use your contact form. This is because many people prefer to email direct (especially if they want a record of what they've sent to you or want to follow up easily). Spam isn't as much of an issue from your email address being on your website (as email filtering typically works well), and there's less risk of messages getting lost.
Most contact form plugins have a reCAPTCHA option you can turn on in the plugin settings, and some have a Spam Honeypot option too.
To check if your contact form plugin has an option for this, head to your WordPress Dashboard, find your contact form plugin, and check the settings page/tab. For some contact forms, for example, WP Forms Lite, you may need to go into the individual form's settings for this option. Contact Form 7 also has other CAPTCHA options, for example, you can set an easy quiz question people have to answer before submitting the form.
If your contact form plugin doesn't offer spam-reducing options, you'll want to install a separate plugin. To do this, go to Plugins > Add New in your WordPress Dashboard and search for a spam plugin such as Clean Talk. Install and activate, and you're good to go.