The name change is one of a number of initiatives Hearn is suggesting in the aim of making League One side Orient “as attractive as possible as a bidder”.
A decision on the future of the £486million Olympic Stadium in Stratford is expected to be made later this month.
“West Ham might not like it but a ground share with Orient makes a lot of sense to the legacy company and for the park," Hearn told the Daily Telegraph.
“You would have the commercial Premier League entity coupled with the local community club serving the community.
“To enhance the point, I am going to make Leyton Orient as attractive as possible as a bidder.
"Now our television rights are around £750,000, not £65million, so commercially we are not as attractive, but we can offer a huge amount as a community club.
“We are going to change the name of the club to London Orient. We are going to give free season tickets to under-18s in London, students and members of the Armed Forces, and free family season tickets to new residents of the Olympic Park housing.
“We are going to try to go from 5,000 capacity to 30,000 by giving things back to the community. We are not interested in making money. It’s very handy but we have only managed it once in the last 19 years.
"We are saying that if we are lucky enough to go up the divisions we will pay more rent, and we are also saying that any profits from the sale of Brisbane Road will be directly invested into the squad to give us the chance to succeed.”
One of the most striking proposed changes is dropping Leyton – reflecting the area of the capital the team are based – from the name.
“Some of the hardcore fans will be grumbling but we have got to do something dramatic," added Hearn.
"That begins with the name change and it begins with opening our arms to a whole new audience.”