1. According to Memory-Alpha, "A Time To Stand" is the only on-screen appearance of a Federation tug.
2. I'd assume the survivors would use a hyphenated name until they got back to a repair facility. Afterwards Starfleet would probably consider the surviving saucer's ship as scuttled for parts and the surviving stardrive's ship as under repair. Once repairs were completed, they would rename the franken-vessel something else (probably referencing twins as an inside joke) and consider the case closed.