"Имя" is a name of a person, a dog, any living being.

"Название" is a name of a street, a river, a city, a kind of animal, a film and etc.

Имя человека. Название улицы.

For a company and a brend, you may use both options.

I would say that you would use "кличка" for a dog or cat in mostly same situations when you would use "it" for it - when it's just some random dog that you don't really care about. At a point where you're well familiar with it, and the pet's personality comes into play and you would use he/she in English, you would also use "имя" in Russian. Though this is not a hard rule, just a trend and it can work differently for different people.

Besides names like streets and movies, "название" can also be used for things like brands, also e.g. in an inventory "название" would be the generic "name" that can be applied to just about anything.

Also note that for people's names, "имя" refers specifically to the first name.

Maks answered correct exept a dog. For pets we use a word кличка.

If you have more questions you can join a WhatsApp group for Russian learners. I have a group for Brazilians who are learning Russian

I just learned Russian so this is my thoughts.   The two are not the same because one is used for how something "is called" Название and what is the name of something.  

I use this one a lot.  " Как это называется?"  this is like "how is this called in Russian?" 

Имя is more for the name of a person, or company.   " Ты знаешь компанию мегафон?" " Да слышал это имя" a

That is what I think but maybe Russians have a better idea than me. 

Natalia, for dogs it is a matter of personal preference. Neither one is incorrect.
And no, not 'pets'. Mostly dogs.
I don't know how do they call cows' and cats' names in villages (is it кличка for cows too?), but I don't think I ever heard 'кличка' form cat owners in Moscow. Unless in documents.

PS. Imagine you ask a name of a turtle and then say "cool name!". Would you use 'имя' or 'кличка'?
PPS. I only know the usage among Muscovites.