Question

Name the tense. At the time she had been living in a rented house ​

Answer 1

At the time she had been living in a rented house. It is an example of past perfect continuous tense.

• The structure of a past perfect continuous tense is as follows:- Subject + had + been + Verb (past participle form) + ing.
• It is used to express events that started in the past and continued until another event in the past. Also termed as past perfect progressive tense.
• Given sentence follows this structure and is thus an example of past perfect continuous tense.    

Answer 2

At the time she had been living in a rented house.

The given tense is "Past Perfect Continous Tense".

Past perfect tense states an action that began in the past and continued up until another time in the past. It is an important tense.

Structure of the past perfect continuous tense:

Subject + had + been + verb-ing + obj

Example: I had been waiting in the queue for 30 minutes before we were told to go home.

There are four past tenses:

1) Simple Past Tense: I went to the park.

2) Past Continuous Tense: I was going to the park.

3) Past Perfect Tense: I had gone to the park.

4) Past Perfect Continuous Tense: I had been going to the park.