good app to record phone calls

[gasparoide]

There is a native one since iOS 18

[RukasuRi]

would screen recording while making a phone call work?

[Sabre11]

Just be aware that in the United States, call recording laws vary by state: 38 states plus the District of Columbia follow one-party consent (similar to Canada, where only one participant needs to agree), while 11 states require all-party (two-party) consent from everyone involved. Vermont has no specific statute and defaults to federal one-party rules. Note that some states (e.g., Connecticut, Michigan, Oregon) have nuances, like civil liability risks or distinctions between in-person and phone calls—always check local details for your situation.

[Sabre11]

Continuing as I thought I should cover Europe too,  the call recording laws in European countries are not uniform and are primarily governed by the EU's General Data Protection Regulation (GDPR), which requires a lawful basis like explicit consent, legitimate interest, or legal obligation for processing recordings as personal data, along with transparency, data minimization, and security measures. National laws add layers: many countries (e.g., Germany, Italy, Spain) require all-party consent for private calls, while others like France or the UK allow one-party if you're a participant and it's for personal use, but businesses often need explicit consent or notification under ePrivacy rules.