Joe Fortemose Chinakwe walked Buhari in an area where support for the president was high, police said.
Officers said they were worried the moved could antagonise people, though he insisted it was meant as a compliment.
He has been granted bail but remains in jail as funds are sought, reports said.
Mr Chinakwe, 30, said that he named the dog Buhari because he had admired Mr Buhari for many years.
"I named my beloved pet dog Buhari, who is my hero," Mr Chinakwe said. "My admiration for Buhari started far back when he was a military head of state."
He was inspired to give his dog the name after reading about Mr Buhari's fight against corruption, he added.
He later told local media he had received death threats over the perceived slight.
Twitters users reacted to the arrest with a mixture of amusement and concern.
"If we keep quiet when they arrest the man who named his dog Buhari who will talk for us when they arrest us for criticizing the real Buhari?" said Reno Omokri.
Mr Chinakwe's case was adjourned until 19 September.