The receiving and sending domain are the same. Can this cause problems?

Yes, it can. If the receiving and sending domain are the same, a newsletter may be rejected or marked as spam. 

For example, the email address of the subscriber has @myorganisation.com as its domain; the sender's address also has @myorganisation.com as its domain.

The email system of the same organisation may then reject the newsletter, resulting in a hard-bounce. The newsletter may also be accepted, but caught by a spam filter. Reason: the newsletter that is directed to your own domain is not internal (from your own servers), but external (our servers).

Whether this will happen in your case can be tested by using a forwarding address with a different domain.

If it is important that the newsletter is also well received in your own organisation, you can ask your organisation's system administrators to do something about this. A solution that often works is to make further changes to the settings of your domain: read more about authenticating your domain(s).

Office 365

In Office 365, these newsletters do not just end up in the spam folder, but are sometimes also marked as potentially fraudulent. ("This sender did not pass our fraud detection checks and may be using a false address"). We have contacted Microsoft about this, and they acknowledge that this is the case, but have no solution for it. The only option is to completely disable these types of checks within Office 365, which is not recommended because this protection against phishing can be very useful.

To be clear: this fraud message only appears when you send email to your own domain and not to the subscribers who receive your newsletter.

The fraud alert can also be remedied by authenticating your domain.