I have an app I want to launch for iphone and for ipad. The ipad version will be used by businesses to input content. The iphone app will be used by their customers on the go to
Yes the app name shouldn't matter unless it's copyrighted by someone else which I doubt.
Since the apps would also be separate, when searching for it on an iPhone, only the iPhone version will show, and vice verca. The only issue you may have is people searching for it on iTunes itself, which may cause in issue with the same names. You could also put on the end of the app name iPhone or iPad respectively. It should still look professional with the added names on the end, and will help out users searching for said app.
Hope this helps.