How can I remove or rename the category called "Other"?

The "Other" category can't be removed because it's used as the default category, but you can prevent links from being submitted in that category by going to the Link Categories setting page, selecting the "Other" category, and checking the checkbox labelled Exclude Selected Category from Submission Form.

If there are no links in the category, and Include Empty Categories is turned off (on the Link Page Format settings page), then the
category will not show up in your link directory.