Is it possible to rename an existing table?

Not at this time. What is the use case? Maybe you can create a new table and upload all the segments to the new one?

One use case would be updating table schemas and ingesting new data without downtime.

You can change the table schema without changing table name. You can always add new fields to the schema, and the old data will be back-filled with default values

Would it be possible to re ingest that old data and have it correctly overwrite the old segments?

Yes, you can always rebootstrap the old data. As long as your boot-strap job generates the same segment names per day/period, they will get overwritten when you push them.