can you identify this plant and tell me how I keep it from taking over the garden?

This is a Phormium possible a New Zealand Flax.
They are thugs in the small garden, you can dig it out but it is hard work, (watch your back) then split it into smaller clumps and then let it grow.
But you will have to dig it up again in say 3-5 years again.

I had one that I split and made 3. i have since dug 2 out and I ended up with 7 which I gave some away.
The others are now in large plastic pots awating a new home.

You can cut the flower stems off after it's flowered.

Snails also love living in the dense growth at the base.

It is Phormium Tenax Tri-colour. They are architectural plants, but do get very big. If you like this type of plant, but don't like the size and care requirement you could try Phormium Cookianum which is a dwarf version of this plant, although much harder to source. Or you could try Astelia, they are lovely plants, come in different colours and have a metallic type sheen on them.

I love Astelia, but you have to be a bit careful with them in the winter, if you are in a cold part of the country, or have a heavy frost - they will need protection!

You can also slice off large chunks with an old bread knife. Unfortunately, 2 years later the chunks are back!! A decision needs to be made! Stay or go!!

I love the Cotinus (purple leaved) against the green and yellow leaves of the phormium, very nice.
As the shrubs surrounding it seem to have got bigger, might be sensible to remove it. If you don't want to, it certainly looks like the shrub to the left could do with a bit of a trim (though I can't see it all in the pic). Treesandthings advice re digging it up, splitting and replanting if you don't want to get rid, and to answer your query re the flowering stems, cut them off at their base when they're finished.