I'm still working on my first world since the nether update.
I created a nether portal, and it spawned in a cave under a massive lava lake. Suboptimal, but I can deal.
The issue is that no matter how far I travel in the overworld, when I create a new portal, it will only link back to that original location in the nether. I cannot get it to generate a new portal in a different nether location that matches the overworld coordinates.
I found one similar issue, but it was old and closed as irreproducible.
Edit: They're saying this is Resolved, but I don't buy it. The issue I reported is still occurring. Regardless of whether it's "working as intended" the failure to generate a new portal in the nether if you build an overworld portal within 1024 blocks is seriously obnoxious, and it's new to the 1.16 update. The updated Nether is much more challenging to travel through, and having to manually place portals on both sides is a giant pain.
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Having this same issue on PlayStation 4

Realized this update probably belongs in a comment, not the original request.
Update 7/5/2020: I was finally able to find an island in the basalt delta to reach the surface.
[media]From there, I bridged out of the lava lake,
[media]and made a couple of nether portals, which DID generate in the overworld.
The first one was at a random location (35, 53, 158) I thought might be close to a village I'd located in the overworld. It spawned above the ocean ~50 blocks from land, on a netherrack platform at elevation 70, which I've never encountered before. The x and z values correspond well to the overworld, but I have no idea why it spawned so far above sea level.
[media]
The second one, I specifically matched to the overworld location (x/8, y, z/8) of a portal I built in the aforementioned village (which had previously failed to generate a new nether portal). It synced correctly to the overworld portal. I had to bridge ~20 blocks out over the lava sea (at y=66) and create a platform and walls to safely build the portal.
[media]
So, it appears portals will successfully sync, IF you build a portal in the nether that matches an existing location in the overworld. There still seems to be an issue with with overworld portals generating an appropriate counterpart in the nether, but I'm starting to think that's because my starting location was over a massive lava lake and basalt delta, and the game couldn't find any other valid locations to spawn the portals.
Next steps: Going to try building a portal in the overworld that corresponds with a known valid location in the nether.

7/6 - Okay, I tried building a 10 x 10 platform, at the right altitude, and then built a portal on the corresponding coordinates in the overworld... no dice. It still kicks me back to the original nether location.
Found the Northern edge of that lava lake though, so I'm going to try one other thing (build an overworld portal that corresponds to a naturally-generated nether location rather than a platform) before I just give up and assume I'll have to build on both sides/link them manually until this bug gets fixed.

No dice. The new overworld portal completely failed to generate a corresponding nether portal, even though the terrain in the nether was suitable and it was over 100 blocks away in the nether. It just synced to the nearest existing portal in the nether.

the same happens to me

Thank you for your report!
We're tracking this issue as MCPE-39609 which has been resolved as "Working as Intended", this ticket is being resolved and linked as a duplicate.
There are some intricacies to portal linking that can sometimes be misinterpreted as a bug. The mod team here as well as Mojang have done significant testing based on the reports that have been made and are unable to reproduce unexpected behaviour.
Please head over to the linked ticket which has a bunch of information in it to help with portal linking issues.
If you believe there to still be a bug, please feel free to head over to the Mojira Discord and discuss it with us in a relevant channel.
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