Lavender

No idea, sorry, about the variety.

Can you remember whether the flowers have little extra rabbit-like ears sticking up out of the top, or not?  The first ones tend to be French varieties; the ones without the ears tend to be English varieties.

You may be lucky trying to move it but it's quite an established plant so there's no guarantees about its survival.  If you do try to move it, the same rules apply as before.  Take as big a rootball as you can without leaving a whopping hole behind, wrap the roots up so they don't dry up, and plant out in the new location as soon as possible (as long as it's not waterlogged or frozen in the ground).