More relevant than whether or not your UG institution is famous is whether or not the department you are applying to knows the institution that you are from---whether they know your LOR writers, and whether they have previously had students from your institution/department who have been successful. There are occasionally excellent departments in certain fields with very famous professors in otherwise less-known schools, and there can be less-known professors and not-as-good departments in brand-name schools. It comes down to how much weight the department you are applying to can give to the different components of your application, and that will depend on whether or not they have anything to compare it to. If your LOR writers have successfully placed multiple students in your prospective program in the past, then her/his word is more likely to be trusted than if no one has ever heard of them. Also in that case, the prospective department can directly compare you to those students, to put your credentials in context. Along similar lines, if your LOR writers are famous/successful researchers with many years of training successful applicants behind then, again there is more reason to trust their evaluation of you. Also important, but not related to brand names: your ability to talk about your research experience in depth, explain what you have done and why it matters, and what you want to do in the future (= that is, your ability to write a compelling SOP). Admissions committees know where the good programs are and who the leading researchers in their field are. These have some correspondence to brand names, if for no other reason than that those schools usually have more resources and therefore they are able to hire more/better researchers and support their students better, but the brand name itself isn't what matters.
soupman got a reaction from UnlikelyGrad4 in SSHRC Doctoral Award/CGS (funding for 2018-2019)