Can I stop my phone from auto-capitalizing names without turning off autocorrect?

On a Pixel, check the keyboard settings rather than only the phone’s general typing settings. If you use Gboard, open its settings and look under Text correction for capitalization and autocorrection options. Those controls may not include a separate switch for unexpected capitalization of names, though, so the exact result depends on which Gboard options are available on your version.

Autocorrect and capitalization are related keyboard features, but they aren’t necessarily the same switch. I’d leave autocorrection on and look for a capitalization or automatic capitalization setting in the keyboard’s own preferences. If it keeps changing specific words, check whether the keyboard has learned or saved those words, since that may be handled separately.

If there’s no setting for the kind of capitalization you want, you may have to choose between living with those changes and turning off more of the keyboard’s correction features. Before doing that, try adding the words you use often to the keyboard’s personal dictionary, if that option is available. It might help with recurring terms while preserving typo correction for other words.