It looks like an evergreen ash. If it is it will get very big very fast. You should yank it now while you can, it's too close to your house.

It lost all its leaves this past winter. Come spring it sprouted all new leaves. We thought it had died but it fully came back

I agree with ash. At our previous house, the neighbor across the street had an ash and I spent countless hours pulling seedlings. They have a deep, strong tap root, and if you are unable to dig the plant out, it can become a battle to get rid of it. Don't delay in taking it out.

I’ll repeat—although it looks like a nice bush now, it will become a problem eventually and could be a lot of work or even expense to remove. Might even damage your house if left too long. I have such volunteers popping up in a hedge which are clipped to the ground every year, but they return, vigorous as ever.