Tree pruning

I thought it looked more like a prunus.
Does it have white flowers in Spring?
As a new build planted tree I would favour a prunus rather than a beech.
I had a wild prunus at the end of my front garden which grew to 30ft plus, it was a wonderful sight in flower. The birds, blackbirds especially, loved the fruit which never grew to any size or were humanly edible.

 

Honestly can't remember if it has white flowers in spring! i think so...

 

That's great, thanks for the link

 

Without trying to worry you, that's an awfully big tree for only 6 years in the ground (even if it was planted at a large size) and I think it's worth considering that if it is a wild prunus, they get absolutely enormous and have a suckering habit. It's not a tree most would advise to have near a house. Admittedly it would be an odd choice for a developer to plant there but they tend to go for the cheapest option on new builds around me and I'm always seeing trees that shouldn't be near buildings.
There are plenty of prunus cultivars that are better behaved but again it's a very big tree in a short space of time, so will likely be one of the big cultivars.

I'm honestly not a cut it down person normally but in this situation I think you may be better to at least consider that option and to replace it with something that would never need pruning like a multistem amelanchier or maybe a fastigiate cherry (there are lots of suitable small trees or large shrubs which you could go for).