I love the nickname [name]Jay[/name] so looking for names we could shorten to this
Can’t use [name]James[/name] 
Some that start with “ja” and the “jay” sound:
[name]Jacob[/name]
[name]Jared[/name]
[name]Jameson[/name]
[name]Jarrett[/name]
[name]Jason[/name]
Some that just start with the “jay” sound:
[name]Jeremy[/name]
[name]Jeremiah[/name]
[name]Jerome[/name]
And, frankly, you are perfectly fine naming absolutely anything that starts with a “j” and just calling him [name]Jay[/name]. People do this all.the.time. HTH 
I love [name]Jay[/name] too! My youngest is [name]James[/name] and I’ve been calling him [name]Jay[/name] or [name]Jay[/name]-bird lately. I agree that any name beginning with a strong J sound would work. I’ve always loved J.P. for [name]John[/name] [name]Paul[/name].
My brother’s name is [name]Jason[/name], but he’s been [name]Jay[/name] all his life. In fact, he strongly dislikes being called [name]Jason[/name] because he is so firmly a [name]Jay[/name].
I know someone just named [name]Jay[/name], but if you are looking for longer names…
[name]Jaden[/name]
[name]Jayden[/name]
[name]Jake[/name]
[name]Jasper[/name]
or any name starting with J