I really doubt anyone in the ENTIRE Kapoor clan is worried about something as pathetic/regressive as "which son will take the family name forward?"
instead of thinking about the overall well being of their family.
Raj Kapoor's lineage has been very well kept intact by Karisma and Kareena in BW, apart from Ranbir.
Yes, daughters can take the lineage forward too.
Because if any logic says they don't, then families with only daughters do not have ANY lineage
.
Btw Ranbir's sister has children too, so I really doubt Neetu Kapoor wants Ranbir to get married just to have grandchildren.
And if we're being technical here, with the whole "family name" being intact...
then Karisma's children still use the "Kapoor" surname. They are as much Raj Kapoor's descendants as Ranbir's children would be.
and what's with the discussion on Ranbir's sexuality?
Did he ever came out as gay/bisexual or anything? NO! Same for Ayan. 
This is exactly what's wrong with our country. If you stay single over a certain age, people will speculate about your sexual orientation, mental health, religious inclination, addiction and what not.
Huge thumbs down to this mentality.
Speculating about someone's sexuality is as bad as "Indian Society not allowing same-sex marriages", if not more.
2