How do you track domain ideas during the naming process?

I'm working on a side project and hit a validation wall. I'd appreciate your honest feedback.

The problem I'm trying to solve: When naming a startup or product, you often search dozens of domain names across different registrars. I've noticed that:

• Most registrars don't save your search history
• Good domain ideas get lost between tabs, notes, or screenshots
• It's hard to track which domains you've already checked

My questions:

1. How do you currently track domain ideas during the naming process?
2. Have you ever lost track of a good domain idea? How often?
3. Is this a real pain point for you, or more of a minor annoyance?
4. Would you use a tool that automatically saves every domain you search and alerts you when one becomes available?

Context: I'm a solo founder building a micro-SaaS. I've done competitive research and read through 50+ Reddit/Twitter threads where people mentioned this problem, but I want to validate with real founders before going further.

What I'm NOT doing:

• Not promoting anything (no links, no product yet)
• Not trying to sell you anything
• Just genuinely trying to understand if this is a real problem worth solving

Would love to hear your thoughts, especially if you're someone who's gone through the naming process multiple times.