While "co-operative" was descriptive, Kennedy told Justice Raynor Asher the name "The Co-operative Bank" had become distinctive.
Kennedy said his client was not alleging or claiming the monopoly of "co-operative" as a word.
No one else in the financial services sector had traded under "co-operative" or included "co-operative" in their brand since Co-op Bank changed its name from PSIS in 2011, he told the judge.
Co-op Bank had spent $8.7 million on marketing since then.
"As a consequence the plaintiff has generated reputational goodwill."
NZACU opposed the interim injunction yesterday and its chief executive Henry Lynch told the Herald it was a fight "for all co-operatives in New Zealand".
He said it didn't feel right for the bank to lay claim to the word co-operative.
"If you're a co-operative and you can't call yourself one, what can you call yourself?" Lynch asked.
Lynch said the NZACU now included building societies and the planned rebrand was part of it becoming more modern.
Justice Asher reserved his decision.
What's in a name
Co-operative Bank
Changed its name in 2011 from PSIS, which launched in 1928.
Has 128,000 customers across the country.
Net profit in the year to March 31 rose to $7.1m from $5.7m 12 months earlier.
NZACU
Formed in 1961 but wants to rebrand as Co-op Money NZ.
As at June it represented 22 co-operatively owned credit unions and mutual building societies.
Its unions or societies have more than 200,000 members and have over $1.3b in assets.