The most common and most likely answer to this crossword clue is the 7 letter word REBADGE
I've seen this crossword clue in The Guardian
R
E
B
A
D
G
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More clues leading to the result REBADGE
Buddy explains!

The straight part
We know that "Give a new name to" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case give a new name to = rebadge.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does REBADGE mean?
REBADGE verb- To market a version of (an existing product, especially a motor car) with a new badge and new name.