Can I name a web application after someone popular?

You need to talk with a trademark lawyer about the exact name you want to use and for what, not about a hypothetical name. You would be looking to get a trademark on the name you want to use. There may be issues of right of publicity as well as of trademark. The right of publicity holds while a person is alive, and in some states, the right of publicity can be retained by the family after the person's death. You would not likely be able to use the name "Lennon" because there are already many trademarks and trademark applications on that name. If you chose a name of a person for whom publicity rights no longer could apply, such as someone who has been dead for at least 70 years, and a name that does not already have a trademark in a similar category of goods or services, you might be able to use the name and get a trademark on it. But that is very questionable and you still need to discuss this with a lawyer and have the lawyer secure a trademark before you count on using the name.

No you can not. Even after celebrities die, their estates have the right to control how their names are used in business.