How do I stop getting obscene text and know if my phone is compromised?

Block the sender.

Block phone numbers, contacts, and emails on your iPhone, iPad, or iPod touch - Apple Support

If blocking fails and if this is an SMS, contact the carrier. If an Apple iMessage, report as spam.

You can also mute unknown callers, which may or may not be feasible for your usage.

Avoid unwanted calls on iPhone - Apple Support

As for hacking… If you’re a dissident, political activist, senior in government or private business, investigative journalist, or otherwise of interest to folks with a whole lot of money, you need better advice. Otherwise, and for the rest of us, and if you’re on current iOS 15.6, you’re probably not worth the effort and cost and your iPhone probably isn’t hacked.

To learn how to better secure your environment, and how we can and variously do get hacked—password mistakes, password re-use, phishing, that sort of thing—see the following document: https://help.apple.com/pdf/personal-safety/en_US/personal-safety-user-guide.pdf

KAPME Said:

"How do I stop getting obscene text and know if my phone is compromised?"

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Troubleshooting Scam Calls:

Three Thoughts:

A. Use Malwarebytes Mobile Security:

The free version blocks popups. Read the following post to see how to use this software: Blocked numbers - Apple Community

B. Modify your Credentials:

If you suspect activity issues, and interacted with it in any form, then modify the you credentials:

• Modify: your login credentials (Using Both a New eMail and a New Password for each and all sites)
• Associate: a different method of payment to your account
• Enable: Two-Factor Authentication for Apple ID and for all other accounts that have such an applicable option

C. Report this to Apple:

Have a Screenshot of this? Forward a screenshot of this as an attachment to Apple using this eMail address: reportphishing@apple.com. In the comments pane, inform Apple of what the attachment is all about: an eMail containing an attachment of a phishing scam. Use my User Tip: Using the Photos App to Report Scams: - User Tips

Do you get spam sms messages? From known sources or unknown sources Did you flag them as spam? Did you contact your mobile phone service provider on the issue? Do get spam sms messages and also iMessages but flagging them as spam often solves the issue - see https://www.iphonelife.com/content/fake-text-message-how-to-report-block-spam-text-messages for example - and I do not get flooded with them. Next step would be talking to the phone company

To check if a phone has been hacked because of really odd behavior requires more technical knowledge, but sounds like your are simply on a spam list or someone is targeting you and with your phone number they can. You could also block the number however if it is text messages you are getting I would think. See Block, filter, and report messages on iPhone - Apple Support

KAPME Said:

"How do I [...]know if my phone is compromised?"

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There is no way to know. The only way it can be compromised might be through a subpoena.

Restore your iPhone:

If you are so concerned, then restore from a backup or reset your iPhone to factory settings. Important: Back Up First: Be sure create a back up your iPhone prior to performing an update, that way you have something to restore your iPhone from, should anything go wrong afterwards. 

A. Restore from a Backup:

Did your ever back up your iPhone with these installed? If so, back up you could back up your iPhone, and then restore it from the backup.

or...

B. Resetting to Factory Settings:

Go here: What to do Before you Sell, Give Away, or Trade in your iPhone, iPad, or iPod touch - Apple Support