I would choose to leave the name alone.
It’s not perfect. The cognate with “Tiddlywinks” is strong, unavoidable for English-speakers, and unfortunate. I’m assuming it was intentional and light-hearted, but trying to introduce it to my conservative company does involve some walking on eggshells.
But changing it is a huge headache, and not merely for technical issues such as redirects and SEO. People get used to something like this and grow attached. A name change, especially to something generic and inoffensive will inevitably lead to some user to assume, “Well, they’ve gone corporate. I guess I’m done.” But it won’t by itself attract new users. (However, if we do go this way, I’ll throw in my idea: something to do with “Minnow”. I image the plain name would conflict with some JS library or other tool. But “Minnowiki” might be available. This has the same idea as “tiddlers”, and we could keep that name or change them to “tidbits” as we like. But I won’t argue this further, since I think sticking with Tiddlywiki is better.)
Two stories:
First, around the same time I started using Tiddlywiki, I also introduced an HTML/JS WYSIWYG editor for business users of a project I was on. It was called FCKEditor. Any English speaker will likely see the problem. The founders name was Frederick C Knabben, so the name clearly had to do with his initials, but anyone fluent in English will probably see a relationship with “fuck”, an often offensive English term for sexual intercourse, widely used in curses. A few years later they realized the name was holding them back, and they rebranded as CKEditor.
Second, about a decade later, I founded a JavaScript functional programming (FP) library. “Lambda functions” are an integral part of FP, and I named the library Ramda. For non-English speakers, a “lamb” is a baby sheep; a “ram” is a male adult sheep; a “ewe” is a female adult sheep. Our first iterations was called “Eweda”. “Ramda” then is a name based on a silly pun. We started this library as an educational playground: could we turn these FP ideas into an actual useful library. But through an odd series of coincidences, it has turned into a very popular (10 million+ downloads per week) tool. Even though the name was just a stupid play on words, we’ve kept it and never regretted it. It helps that my co-founder’s wife is a professional illustrator and was able to create a great logo, but there simply was never a good reason to look to change this name.
The difference: Ramda’s name is playful. FCKEditor’s sounded positively offensive to some.
I think Tiddlywiki’s case is much closer to Ramda than to FCKEditor. Yes, “tiddlywink” can have a derogatory tone, but that is a secondary association. I imagine the initial association for most users who have one at all is with the game. That just makes the name light-hearted. For the smaller number of others, I don’t find changing it to appeal to them will offer enough benefit to overcome the hassle.