Your thesis is a publication, and unless you have strong reasons to do so otherwise, I would recommend that you use the same name in all your publications ─ be they theses or papers.
I would particularly recommend that you do not pay attention to the oft-propagated myth that "nobody reads PhD theses". For one, it's simply not true (at best, it is field-dependent), but more importantly, it is irrelevant. Regardless of whether people read your thesis or not, it will appear in both your CV and other publication lists (Google Scholar, ReseracherId and ORCID, at the very least). I think the core question there is: what name will you use at the head of your CV?
- If you'll use your maiden name, with only an incidental mention of your legal name when required, then it makes no sense to have any publications under your legal name.
- If the header will be your legal name, then it still doesn't make sense to have some publications with a different, maiden name (the papers) and some with the legal name. You still have to design around the use of two different names, and using the legal name for the thesis only complicates that design even more.
I was under a roughly similar situation, where my UK university required a legal name for the PhD thesis that differed from the name I use for papers (specifically, I left out the maternal surname), and I can tell you that the legal name did propagate to places where I would rather have one single unified front.
More importantly, though, I think that the key distinction is that the PhD diploma and the PhD thesis will be seen by two drastically different audiences.
The PhD diploma will probably only be seen by Human Resources staff, or their equivalents, who are trained to deal with this, and for whom person-changed-their-name-through-marriage is a run-of-the-mill type of feature. Having a legal name that differs from that on your PhD diploma, with a marriage certificate to match, won't even raise an eyebrow.
The PhD thesis, and particularly its bibliographic details, will be seen by a lot more people, and they will have a lot less incentive to care about the details - it's more likely to confuse them and they're much less likely to chase it up to figure it out.
After having said all of which, though: It's your name. It's your choice. Consider all the points that everyone has mentioned here, but do what feels right to you.