Not showing full name in the tabs in site

I don't think so. You would have to minimize the name of the tab. 

what if there is such requirement that you have to show the full name ?

As of now, the only option is to shorten the tab name as suggested by Konduru Chaitanya 

I would recommend you make the business understand the boundaries that we have here and have a name that fall in the acceptance criteria. 
If it seems to be so important than you can think about a work around for having tabs in a interface. But this is not so recommended as we have tabs under site which gives better UX.

I would recommend you make the business understand the boundaries that we have here and have a name that fall in the acceptance criteria. 
If it seems to be so important than you can think about a work around for having tabs in a interface. But this is not so recommended as we have tabs under site which gives better UX.