Not easy.
You could use Tairua if you are going for a literal translation.
That is Logan means Valley/hollow in Gaelic and so you could translate it to Tairua, using a Maori word for Valley or Hollow. However the English ear would fail to see a connection between Logan and Tairua.
There are other possibilities. There are a few Maori words that can be translated to hollow/valley.
You could find out the Aboriginal Name for the area and "assimilate that word, as Maori" or literally translate their meaning.
The Logan region was originally inhabited by Aboriginals from two major language groups; the Yugambeh and the Jaggera.
You could describe it as "Tangata Whenua YugambehJaggera" as a LOAN or borrowed creative cojoin.
It is hard to Loan or convert Logan to a Maori word Like Apple and Aporo.
It kind of depends on your application. You can make reference to the traditional owners or you could just usurp the word Logan and use it. Te Logan or Whenua Logan???? Not the prettiest solution but maybe the easist.
I think the best solution is to discuss the issue with traditional native landowners and get more background.
Good Luck.
The Maori word for "Logan" is Rōkana.
Tuhinga
The Maori name for Desmond is Hēmānia.
The Maori name for Margaret is Mareta.
The Maori name for Manukau is Manukau.
The Maori name for Finn is "Pine" and the Maori name for Jake is "Hemi."
The Maori name for legs is "waewae."
The Maori name for Margaret is Mareta.
The Maori name for Desmond is Hēmānia.
The Māori name for tui is "pīwakawaka."
The Maori name for Manukau is Manukau.
The Maori name for John is Hone.
The Maori name for the planet Mercury is 'Takero'.
The Greek name for Logan is "Λόγκαν" (pronounced as "LOH-gahn").
Randy Logan's birth name is Randolph Logan.
the name of the Maori tribal leader was Rangatira.
The Maori name for Banks Peninsula is Te Pataka o Rakaihautu.
Kakapo is the Maori name. It means "night parrot".
Piwaiwaka or piwakawaka.