Yes, a number of licenses explicitly allow reasonable attribution notices that must be preserved.
The Apache 2 license has the concept of a NOTICE file that must be made available to users, but not necessarily in a prominent place. It is sufficient to show them “wherever such third-party notices normally appear”.
The GPLv3 has a mechanism for Additional Terms which can be used to require the preservation of notices (section 7). However, the notices must be reasonable, which probably excludes a requirement to show them prominently.
The niche but OSI-approved Attribution Assurance License requires that some text is shown in the documentation, and in a prominent place upon launch of a program (e.g. a splash screen). However, the AAL is about ensuring attribution of original authors, not necessarily of a project.
It is easy to see how excessive attribution requirements could be abused to the point that such a software is no longer free. For example, there was a web application which required modified versions to show the original project's logo on every page. Such “badgeware” cannot be open source when it triggers attribution requirements on mere use of the software. Such requirements are only OK if they apply to derivative versions of the software.
Attribution requirements were actually a topic on the OSI's license-discuss mailing list in December 2018. You can read my summary here.