Voyager's original Chief Medical Officer was an unnamed human lieutenant, played by Jeff McCarthy.
The Doctor being used for far longer than he was designed resulted in some issues with his program. It started to break down and act unpredictably, and not always in particularly useful ways. As such, his subroutines were altered during the journey, and the Doctor sometimes even made these changes himself. These tweaks, paired with his experiences, contributed to the Doctor's sentience and personality changes. If he'd been left as the last doctor standing in the Alpha Quadrant, he would've only been left in service until Starfleet assigned replacements to Janeway's crew.
What Would Have Happened To The Doctor If Voyager Hadn't Been Stranded In The Delta Quadrant
The first version of the EMH was quickly deemed unfit for service
Because Voyager originally had a full complement of medical personnel before being sucked into the Delta Quadrant, Picardo's character began as a contingency plan stored in the ship's computer. The EMH was for dire circumstances only, so it stands to reason that he may have never been required in the Alpha Quadrant, and if he were, his stints of activation would only have been comparatively brief compared to his workload on Voyager. That said, Voyager's doctor was just the first iteration of the EMH, and there were certainly some wrinkles to iron out.
Picardo's cameo in 1996's Star Trek: First Contact proves that the EMH MK I was installed on other Starfleet ships.
The EMH MK I was designed by Dr. Lewis Zimmerman, who was also played by Robert Picardo. Zimmerman based the first EMH's physical appearance and personality on his own, but his brash nature and arrogant attitude weren't exactly great traits for a doctor. Starfleet quickly decided that a new EMH was required to replace all the original copies, and so they were repurposed for manual labor, often given tasks like working in dilithium mines and scrubbing plasma conduits. Voyager's doctor avoided the fate of his Alpha Quadrant counterparts thanks to being stranded in the Delta Quadrant.
Immortality May Also Be A Curse For Star Trek: Voyager's Doctor
The Doctor is confirmed to still be in existence in Star Trek's 32nd century
The Doctor is a fascinating character whose journey is unique within Star Trek canon. There have been other sentient holograms within the franchise, but none have grown anywhere near as much as the Doctor. As an artificial lifeform, Picardo's character is functionally immortal, and the salvaged mobile emitter from the 29th century allows him to move freely like any flesh-and-blood character. For all of the perks he gained, the fact that he could live forever suggests a pretty macabre existence after Star Trek: Voyager.
Picardo will appear in Star Trek: Starfleet Academy, and the upcoming show takes place in the 32nd century. Given that the Doctor has been online since the 24th century, the events of Star Trek: Voyager will have been a long time ago, and he will have been forced to grieve the loss of Janeway and her crew along with any other individuals he has bonded with since. That said, Picardo has said that Starfleet has pulled his character out of "holographic mothballs," so it's unclear if he's been continually active since his debut in Star Trek: Voyager.