How do you cope with someone calling you to come back every time you step out of the room?

I did elder homecare for a very long time and have known many families with exactly the same problem as yours. An elder who must have someone in the same room with them 24 hours a day.
I will tell you what I've told every one of them and it works.
You and your mother have to ignore her sometimes. When she calls continually do not answer her every time and do not go running to her.
When it's time for her to go to bed you and your mom's "shifts" are over. The only thing you do for her at bedtime is give her some water or take her to the toilet a couple of times and let that be the end of it.
This situation is similar to having a baby. Mom shouldn't go running in every time the baby squawks a little. Sometimes you have to let a baby cry a bit. It's good for them. If mom goes running in every time the baby makes a sound, they will never be able to be left alone. The same applies to elderly people. Even ones with dementia. I'm sure this will be hard for you and your mom, but you're just going to have to let grandma squawk a bit. Other wise one of you will have to stay next to her 24 hours a day.
You can arrange her environment in a way that helps. Leaving a tv on for her set to a channel that plays all the old shows 24 hours a day. Or a radio with nice music playing low enough that she can still go to sleep at night. Making sure her room has a nightlight on.
Or her doctor may prescribe anti-anxiety meds to help her.
You and your mom have to stop running to her every second. That has to stop because the two of you will get worn out quick. Good luck.

I believe this phase is part of "shadowing". I just experienced this on a recent trip out of state to help my 99-yr old aunt with mod/adv dementia and her 102-yr old sister who has almost no cognitive or memory impairment. They lived their whole lives together and the younger one (who is not very mobile) yells (sometimes screams) continuously for my other aunt every time she leaves the room. It's a small house so hard to get away from it and my poor auntie can't help but respond. We have to ignore it. The other tactic we tried is to seat her in the kitchen where we were spending most of our time. We gave her "tasks", such as folding a large pile of kitchen towels, sorting colored poker chips and sorting and pairing socks. As long as she wasn't yelling for "Anna!!" continuously we could manage. Good luck with this!

When my husband who had vascular dementia first came home after almost dying from aspiration pneumonia, and was completely bedridden in our living room, he would do the same thing. He was calling my name constantly, and we live in a small one level house, so it wasn't like I was going far. I would always before I left the living room tell him exactly where I was going and why, thinking that would help, but it didn't. It was driving me crazy, and so I mentioned it to my local caregivers support group, and one of the seasoned caregivers told me that it was probably because he was afraid, as he was now bedridden, and just wanted to know that I was near. That changed my perspective, and over time he only called me when he needed something.

If grandma is stuck in a room off by herself, you may want to try putting her in a more centrally located room, such as the living room during the day, where she can be part of the action, and then bring her back to her room at night, and see if that won't help.

Nurses and CNAs in hospitals often seem to have developed advanced skills in ignoring this kind of calling out. Beats me how they do it! - I haven't yet got to the stage where I can just blank someone who's asking for help, or even just attention.

How does your mother cope with it?

It does look as though you're going to have to divide your grandmother's calls between two lists: needs, and wants. Once you're sure she has everything she Needs, it will then be up to you how often or how quickly you respond to what she Wants. Got any earplugs or noise-cancelling headphones??!!

Also - as long as one of you is in the room, is your grandmother then content, does she stop calling out or asking repetitive questions?

Since you know that she doesn't actually need anything, can you just ignore the calling out?

It seems that this may be a symptom--anxiety, agitation, that might be addressed with meds. Talk to her doctor.

Think about it, you have no idea what is happening to you. Your world is strange. You don't recognize it. Your scared to be alone. So of course you want a familiar face.

Is there a reason grandmom needs to stay in her room all day?

I see two primary issues, either or both of which could be present.   Those who wrote on the need to be with people offer excellent insights.    The fear of being alone can be overwhelming.   OTOH, there could be manipulation involved, in which case, taking  a stand against being there constantly might help. 

But w/o knowing which issue prevails, I'd be inclined to think that the dementia is the dominant factor, with a touch of controlling needs.  She's losing cognizance, perhaps awareness of where she is, and is fearful.   And that can also contribute to her need to have people she knows around her.

I second the suggestions to bring her into areas where she's not alone, and try to find ways she can interact despite her dementia.   The "folding towels" suggestion is raised here periodically; that might be an option, depending on the level of her dementia.

I’ve noticed something recently that I actually learned in college, but have recently been reminded of by my cherished LO, who has survived 2 Covid infections.

When I first began visiting after months and months of being away from her, she would repeat “Please help me, please help me, please help me……” endlessly, when there was nothing obvious that she needed. I think her current neurological status makes it difficult for her to put the verbal brakes on.

My reaction was to tell her I’d help her if she needed something and then immediately launch into a conversation about something interesting like grandchildren, weather, clothes, family memories…..whatever.

As I visit more regularly now, I notice that she doesn’t seem to need to be doing this nearly as much as before.

Does she dress and come out of her room? Maybe if you inundate her with chat, she’ll welcome being quiet a little bit more than she is now?

I agree that she is probably afraid to be alone because while she doesn't know what is happening to her, she knows deep down something is off making her very afraid.

I also agree if she is in a more central location where she can see you and your mom while taking care of other tasks. Does she like music? Maybe when you have to leave if you can have some soothing music for her to listen to while you are away. Also, leave her for short periods and try and build up the time away from her. The only other thing is to make sure her needs have been met and ignore it for a while.

Maybe its time to try another medication to take the edge of the agitation. Realize it can take a couple of weeks for the drugs to build up in her system; but keep on the drs until something is found that works.

I wish you all the best.

My 97 yr old Dad with Dementia is like that. He feels more comfortable when someone is in the room with him. Like a little child feels comfortable sleeping with their parents.
I purchased a real soft tufted Automatic Recliner and for the last two years, my Dad has been living in the Den where the TV is and is where the action is.
He likes sleeping in his automatic recliner and it is easier to get in and out of then his bed and he's never had a bed sore. I also purchased a seat pad for his recliner.
His feet don't swell either, because they are always elevated.
So much easier to transfer him out of the Recliner into his wheelchair.
You should try that with your Grandmother. At least during the day.
I think my Dad was just scared being by himself.