If the name is less than 6 characters, we cannot edit the question. Where as, editing that question is important as leaving signatures is not allowed at SO.
First, it's not "not allowed", it's (strongly) discouraged. A signature or "Thanks, xyz" is noise, and removing it improves the signal to noise ratio, so it's a good thing. But a signature or thanks is not in any other way bad, it's not offensive, it doesn't make the question unclear. All it does is unnecessarily occupy a bit of screen space.
So I don't think it's important to remove signatures and thanks. Desirable it is, but if a signature stays on a post, I don't consider that a serious problem.
That doesn't mean I will always reject suggested edits that only remove a signature/thanks, but I won't approve all such suggested edits either. It depends on how the rest of the post looks. We have the canned rejection reason of "too minor":
This edit is too minor; suggested edits should be substantive improvements addressing multiple issues in the post.
An edit removing only a signature fails on the "multiple issues" part, but that's in general not taken as an inviolable law. If there is only one issue with the post, we're perfectly happy if a suggested edit addresses only that one issue.
The "substantive improvement" requirement, however, is more serious. Is the removal of the signature a substantive improvement of the post?
Well, there are those who say any improvement is substantive enough to approve the suggested edit, there are those who say any suggested edit should try hard to make the post perfect. As you can see in the answers to older questions about minor edits, e.g. Should tiny edits be accepted or rejected in review? and An alert to serial minor edits, the community is divided.
I think most reviewers fall between the extremes and will judge the edit against the post quality before and after.
Does the suggested edit significantly reduce the ungoodness of the post? If yes, approve, if no, reject¹.
So the answer to your question
How to overcome this?
is: Take a look at the entire post. In the vast majority of cases, there are enough issues you can improve that the six-character limit isn't an issue. If you² don't even try that, removing the signature is a waste of time and the limit preventing the submission of the edit is a good thing.
Now, occasionally, there may be the rare post where you can't do more than remove the signature, and the signature is too short to pass the six character limit. I haven't ever seen such a post, but it's conceivable. In that case, regretfully leave it be. The post is still a rare gem with the signature. Sooner or later someone with full edit privileges will polish the last speck off it. Or perhaps not, doesn't matter if the post is so good that you can't find six characters to improve.
¹ We now have the option to improve and reject, yay!
² Generic you, not you personally.