I want to start an OpenSaaS software company for a software say WordPress. Something like Wordpress.com. Do I need to mention which software is being used behind the site, and what are the other requirements to get started?
I don't think there's a general answer to this question: it will depend entirely on the obligations placed one you by the licence(s) that apply to the software you are using.
In the case of wordpress, this is GPLv2, which as I read it (and IANAL/IANYL) does not require you to announce that you're using the software as part of your SaaS.
Edit: in the case of sentrifugo, their website says that's under GPLv3, which also (again, IANAL/IANYL) I do not read as requiring that you announce your usage of it.
If you were to use software published under, say, the Affero GPL v3, and you were to modify it in order to provide your SaaS, the licence would oblige you not only to notify your users, but to make the modified software available to them (and the rest of the world) for download.
In the case of proprietary software, there are generally no such obligations. I have been involved with any number of big websites built with Oracle as a backend, and our obligations to Oracle began and ended with us giving them about 3.2 metric wheelbarrows full of money (and sending more of the same every so often). But again, you should read the licence.
So once you know exactly what you intend to do, read the licences (or better still, pay for qualified legal advice on the licences) and then honour any obligations you believe that you have. Whether you have a moral obligation to credit the software on which you are building your business, especially if it was provided to you with free-software freedoms and at no cost, is not within the remit of this site.