The spell description is unclear, and it's a downtime/world-building activity anyway, so ask the DM.
Teleportation circle says:
You can create a permanent teleportation circle by casting this spell in the same location every day for one year.
It is simply unclear if "you" here restricts who can create the permanent circle. Is it only "you" who cast the spell first, or is it "you" whoever happens to be casting the spell today? Who's to say?
The DM, that's who.
Creating a permanent teleportation circle is a downtime activity. It requires buy in from the party, the DM, or (most often) both to be able to do in the first place. Either the party has to all agree to spend a year returning to the same place every day, or the DM has to agree to get an NPC involved in doing that. This is simply not a question for mechanics. It's a question of narrative, so it's up to the DM as the master story teller, with input from the rest of the players when it will involve downtime.
The answer to this question should not be a surprise.
Michael W. left a comment that captures perfectly how a player and DM should go about handling this situation:
The one thing I'd add to this is that the PC with the spell almost certainly knows the answer to this question in-game as well, so it should be completely fair game to ask the DM before the PC selects the spell, plans resources around getting the circle up, etc. the answer should not be surprising to the PC!
This is very similar to how I handle the wish spell. Wish presents the players with the opportunity to permanently alter the game world, and so a DM should engage with the players on what the looks like. In the same way, teleportation circle gives the wizard a chance to permanently alter how the world looks - it can provide an anchor point for the party’s travels throughout the land. This is an opportunity for the players to engage in a bit of worldbuilding, and this is the sort of engagement that I love to encourage.