Please Help My Tree

Please Help My Tree

If anyone could help me identify this tree I'd appreciate it! We've lived here for about 8 months and I think it's actually begun to look "sadder". I started deep watering it a few weeks ago and that's helped a little. It also has some dead braches on it but I don't know if I should cut them off or trim them. Any help or advice is welcome!!
New place!

New place!

i havent posted here in like, a year.

i havent posted here in like, a year.

Jerusalem artichoke

Jerusalem artichoke

3 rooms!

3 rooms!

It’s spring!

It’s spring!

A Positive Garden Note

A Positive Garden Note