Su.Ki., in China, there are tertiary education institutions named "[district name] University for Old People", a legacy from a time when China was not practising market economics. Now, as you said, they need to think about consumer psychology, and they are changing their names to "community college", "open university", "college of continuing education", etc. Yumia, you will have seen that these colleges are all in the process of changing their names.

There is such a thing as 'The University of the Third Age', but I don't know how widely this term is used. I doubt if anyone would sign up for anything with 'elderly' or 'old' in the name. 'Old' has negative connotations. 'Elderly' is gentler, but suggests someone of around 80+. These words would put people off - nobody wants to be thought of as 'old'. The word 'senior' is often used to refer to retired people, particularly in the US, as it is more positive in tone.

university for the elderly

university for the elderly