Q. “What is the exact meaning of Ram and Hare in mahamantra?
If Ram is Lord Ram then how we are connecting Radha’s name with Ram?”

A. Krishna and Ram are addressed to the Supreme Lord in Hare Krishna Mahamantra.
‘Krishna’ meaning the ‘all-attractive’ and ‘Ram’ means the ‘reservoir of all-pleasure’.
‘Hara’ is the pleasure potency of the Supreme Lord, termed as ‘Hare’ in vocative.
So the meaning of Hare Krishna Mahamantra is a prayer to the Supreme Lord, who is all-attractive and reservoir of all-pleasure to enagage us in His loving devotional service.
Some other places, Srila Prabhupada refers ‘Ram’ to Lord Balaram and sometimes Lord Nityananda.