Currently to propagate the change of header text to header links, an explicit user interaction is needed that involves opening a modal window.
It would be great if this change is detected automatically/inline and no explicit user action/dialog is necessary.
A related FR that is similar to implement:
This is something that more realistically can be implemented:
https://forum.obsidian.md/t/add-markers-in-the-gutter-for-headings-and-blocks-that-are-referenced-somewhere-else/37708
The original FR has 83 upvotes.
Please make this happen - as a full feature … not a right click situation.
@toiteam : I have also been dying to have this feature. In fact, I am surprised it is still outstanding even though it is a basic requirement. The right-click ‘solution’ is just a workaround, but of not much use.
Still, this request only has 8 upvotes (see OP at the top of this page), so will it ever be implemented???
Made an account to like and comment on this issue. As I use internal links in headers, and just did a note name overhaul, essentially all of my header links (which are the main way I link) are broken. This is causing serious frustration with Obsidian/reconsideration of using Obsidian, please fix. Been great otherwise.
@shinyben : you make a good, and very important point. I have the same frustration after using the Numbered headings plug-in for a while.
There is light at the end of the tunnel, though, because this is now on Licat’s short term road map.
Woot! 
#save-a-click_save-a-life
At least in the backwards, 1980’s, f-key driven, MS-DOS based world of the modern Electronic Health Record (EHR)…
Imagine Sarah McLaughlin singing “In the arms of the angels,” but with sad doctors and patients instead of neglected puppies and kittens…
Non Sequitur Sundays!
(But for serious, we must automate to liberate [from the clicks]… Even in the manna that is Obsidian)
+1 small vote for Homo habilis and Obsidian tool goodness
+1 large vote for Homo sapiens sapiens and its war on clicks
(Also, +1 for das feature)
I have it from the horse’s mouth (Licat’s) directly:
Preserve links after renaming headings has already been implemented - you just have to trigger the rename using the right click menu on the heading. Blocks don’t get renamed often so we haven’t prioritized it.
My reply:
The right click trigger is not workable in practice. You have to remember to do it. It should be an automatic thing, like the automatic adjustment of links when file names are changed.
Licat’s explanation:
Unfortunately, monitoring heading changes automatically is impractical from a performance perspective. Automatic rename would mean that the program has to constantly monitor what you’re typing in the document.
Constantly checking if you’re editing a heading or not a heading, whether that heading has references to it. It also doesn’t know when your rename is finished.
So, that means this feature request will never be implemented natively in Obsidian. @WhiteNoise can therefore close this topic.
This is something that more realistically can be implemented
Huh, I vaguely thought that links and headings were indexed, and so could be updated at least when the page saves. Also, “Preserve links after renaming headings and blocks” is on the short-term roadmap (as pointed out by @I-d-as), so I’m not sure what that means.
I would never have thought to use a context menu to rename headings. I’ll try to remember to do it, but I don’t expect much success.
It means a rename block (similar to rename header) will be added. I understand it is confusing and will be renamed.
@CawlinTeffid Sorry to mislead you. All this time, I had been thinking, in the works, was a feature that immediately automatically updated links to a heading when it was edited. I hadn’t seen this thread obviously. The problem I have with the context menu is forgetting to use it or accidentally editing headings. Still processing this. Oh well. Better to know than not.
It’s not your fault, I do think the trello card was poorly worded (for brevity).
Check out Block-reference-count plugin, it’s a good solution for knowing when to use the rename functionality and maybe some of that will be implemented in core.
Thanks. Feeling better already.
The Block-reference-count plug-in has the problem Licat referred to when he answered me about the automatic updating of links to headers: it slows down Obsidian. I used the plug-in, and noticed that when you type there is a distinct, irritating lag before the text is rendered.
The dev went through several iterations to improve it, which he did, but a lag remained nevertheless, so I gave up on that plug-in.
I know you saw me make this comment in Discord, but I just repeat it here for others.
@CawlinTeffid the context menu to adjust links to headers is useful if you just change one header name.
I use the Number headings plug-in, which adds a number to all of the headers and subheaders in a note. If you then add or delete only 1 header, the plug-in adjusts all the header numbers on that page, bypassing the context menu.
The problem for me isn’t how many headings I want to change, it’s that headings are part of the text, and I change text by selecting and typing, not by right-clicking. When I inevitably click a broken block/heading link, I suppose I’ll be able to find the text and update the link without too much work, it’ll just be an annoyance. (Just clarifying, not expecting any action.)
@CawlinTeffid I agree with that, and that is what I told Licat in the Discord discussion yesterday. I have used the right-click option once, even though there have been instances where I should. I just forget to do so, probably because, as you indicate, it is unnatural.