Han and Leia naming their kid "Ben" made/makes no sense.
Han knew Ben Kenobi on a very limited basis. During their initial meeting, Ben basically played Han in Mos Eisley by negotiating the deal for the flight to Alderaan down and paying very little up front (and ultimately not paying as much up front as originally promised since the speeder didn't sell for as much as they hoped).
On the Death Star, after Ben tells everyone he is going to go disable the tractor beam, Han affectionately refers to Ben as an "old fossil." Han later seems to display some skepticism as to whether old Ben was up to the task of disabling the tractor beam (saying something to the effect of "let's hope that old man took care of the tractor beam or this will be a real short trip").
In sum, Han knew Ben Kenobi for the equivalent of a few hours (i.e. original meeting in Mos Eisley, travel to Alderaan, minutes on the Death Star). Ben was talking with Luke the whole time/training Luke on the Falcon. Han is not Force-sensitive. Ben and Han simply have no connection.
Leia has never seen "Ben" Kenobi, other than a possible fleeting glimpse of him fighting Vader on the Death Star as she ran into the Falcon. Leia sent a message to "Obi-Wan" because her father (Bail Organa) either told her to or told her about Obi-Wan possibly being able to help the Rebellion. Leia didn't see Obi-Wan/Ben appear as a Force ghost at the end of ROTJ, as only Luke did (I suppose the reason why she didn't/couldn't see the force ghosts is debatable, but it's not material to this point).
After the Falcon left the Death Star, Luke was very sad that Ben had "died" (by becoming one with the Force). Leia comforts him during this time, but this has nothing to do with Ben dying... this has to do with comforting Luke, who was the one (along with Han and Chewy) who saved her.
Thus, neither Han or Leia have any meaningful connection to "Ben" Kenobi. The only person who has a meaningful connection to him is Luke.
It's implausible to think that Luke had enough "power" over Han and Leia that he could convince them to name their son Ben. Even if he did, this is also problematic, as Luke referred to "Ben" as "Obi-Wan" in ROTJ when Obi-Wan appears as a Force ghost after Yoda "died." Luke later refers to him as "Ben" during the ensuing conversation, but, at best, this shows that Luke views the names as interchangeable. There is no reason to believe that even Luke has a strong connection to the name "Ben."
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