Can a news outlet publish my name or photo?

Art. 85 obliges every member state to reconcile data protection with journalistic expression — so news reporting runs on national media law and press-council codes more than on the GDPR rights you use against shops. What that means in practice: reporting on matters of public interest may name and show people without consent; the balancing (Strasbourg’s Axel Springer/Von Hannover line) weighs contribution to public debate, your role (public figure vs private person), how the material was obtained, and the intrusion’s severity. The lines that survive the privilege: private persons swept into news enjoy stronger anonymisation claims; several countries’ press codes anonymise suspects (initials, blurring) until conviction; victims — above all minors and victims of sexual offences — get near-absolute protection; and long-past reporting resurfacing in search engines is exactly what de-listing exists for: the article may stay, the name-search result may go. Your realistic routes: not an erasure demand to the newsroom (the privilege usually defeats it), but: the outlet’s corrections desk for factual errors, the national press council or media ombudsman for code violations (free, surprisingly effective), de-listing for outdated coverage, and defamation law where reporting was false. Content farms and “news-shaped” shame sites flunk the journalism test — against those, the full GDPR toolkit applies, no privilege attached.