Using as isn't strictly ungrammatical, but it's not standard usage in this sort of sentence; just use named ABC.
You should use the commas. In this sentence, named ABC is what's called non-restrictive: It doesn't serve to limit the identification of method, whose identity is already clear. Non-restrictive phrases, like this one, are set off in commas; you could strike out everything between the commas, and the sentence would still be clear. Restrictive phrases are necessary to properly identify the item being described and are not set off in commas.
This method, named ABC, is used to calculate the temperature of these categories of objects.
The demonstrative adjective This clearly identifies which method you're talking about, so named ABC is extra information that's not required for the sentence to make sense.
The method named ABC is used to calculate the temperature of these categories of objects.
Unless which method is clear from the context, you need named ABC so the reader can tell which method you're talking about, so the phrase is restrictive; no commas.