I'll start:
- Looking up quotes about whatever the product is for, e.g. photography quotes for a portfolio building website. This helps me get a feel for how people who really love the subject area talk about it.
- Google's Keyword Planner. This puts me in an SEO mindset from the start and helps me see related words/phrases that may make good product names.
What techniques/advice do you have to share about coming up with product names?