Multiport female connector

The connectors shown have a female form factor and are rectangular in cross section, rather than circular. “female rectangular connector” might be a good search term to summon the product family of likely interest.

It’s got a single row of contacts, a countable number of positions, and a measurable pitch. Those would be logical next selections to narrow things down.

Assuming 0.1" pitch and limiting to things with photos that can ship reasonably soon, some options that look promising start to show near the top.

I would suggest however, that attempts at replacement may be inadvisable unless the connectors are demonstrably faulty. That assembly was not designed to be repaired, so “fixing” things that aren’t genuinely broken only increases the probability that you’ll end up looking for a donor.