Your passport will be valid for less than a year after you are done with your interview and other visa processes which isn’t good. Once you arrive in Germany, you will be required to extend your visa. You might be given a one year or two-year visa extension depending on your city. However, the duration of your extension is also dependent on the validity of your passport. If you have ten months left in your passport and the Immigration Office is supposed to extend your visa by one year, they would extend it by ten months because your passport is only valid for ten months. In the same way, if your passport is valid for a year and the Immigration Office is supposed to extend your visa by two years, they will only extend it for a year.
It is therefore important to apply for a new passport after June 16th, 2018 as per Indian government rules. You should go ahead and present your old passport on June 22nd at your visa interview as it is still valid. I don’t know how long it takes to get a new passport in India, but if your new passport arrives before your visa is issued, you can simply contact the embassy and submit your new passport along with its details to them. On the other hand, if your visa is issued in your old passport before your new passport arrives, it’s not going to be a problem since according to Indian government rules you can have two valid passports if one is close to expiration. Your new passport will satisfy the three months passport validity requirement, and I’m pretty sure your old passport will fulfill it as well by the time your visa is issued, and you leave the borders of your home country to Germany. You should therefore not be worried about being denied boarding.
Once you arrive in Germany and decide to extend your visa at the Immigration Office in your city, it is essential to show your new passport. If you don’t, your visa will be extended for a shorter duration than the usual length.