Is there anything called a personal plan?

[Shabah7]

I want a plan that is less than the professional plan just to connect my own customized domain.

[Valentina]

You can learn more about the Square Online plan options on this page!

The Free plan is the step below the Professional plan, but does not support the use of a custom domain. You'll need to stick with the Professional plan in order to use a custom domain, @Shabah7.