Yes and no.  BT devices like headphones love to be connected up to ONE
device....and only one.

If the headset is paired with your sellphone, you'd have to repair it,
every time, to use it with your laptop and every time to pair it with your
desktop.

If the headset is paired, already, with your sellphone....and the sellphone
is already running....it will pair with the sellphone and you'll have to
unpair it, or easier turn off the sellphone before turning on the headset.

If the headset comes on and DOESN'T find the device it wants to connect to,
then it will go into FIND ME and start broadcasting for pairing so your
laptop can find it.  You can then pair it with the laptop and from that
time on it will try to look for the laptop....ignoring the frantic calls
from the cellphone trying to pair with it the next time the sellphone sees
it is on.

So, the proper procedure to prevent the frantic calls from the last device
it was paired with is to UNPAIR with the headset....then pair the "free
from pairing" headset with the new device.

This is done to make pairing automatic with one device....and that works
great.  But it sucks as it will ignore all others.  There's no solution I
know of.