@Willem-Maroon-Llama#247592 SMS text messages are fundamentally insecure, even worse than e-mail in some regards. Anybody can spoof the sender name, that's just how the system works unfortunately. When you block the "bunq" sender, you also will block legitimate text messages from bunq, as there's no way for your phone to distinguish between what is a real and a fake sender name (there's no such notion when it comes to SMS). Therefore it might be counter-productive.
What you can be sure about is that bunq will always use their own domain bunq.com for hosting any important websites. Any SMS or e-mail that leads you to page that doesn't belong to bunq.com is highly likely to be a phishing attempt. Other than SMS sender names, the communication between your web browser and web servers is usually protected quite well and spoofing anything nearly impossible for a fraudster.
And if in doubt: contact bunq Support through the in-app support chat first before doing anything else. The official bunq app has extra protections to make sure that the information exchanged through it is encrypted and is only accessible by you and bunq itself, and no third-parties. That's also the reason why bunq will reach out to you via the app if there is any issue with your account, and not via SMS or e-mail (they certainly wouldn't include a link leading to a login page).
Some more good tips and knowledge about phishing: