I'm so upset..
Don't be upset
. This is just a minor glitch. Given that you're about to apply for ILR and your visa is expiring soon, I don't think the name change will be an issue.
All you need to do now is focus on studying for and passing the Life in the UK test, and then applying for ILR before May 3rd.
Ideally, you want to get your ILR application submitted sooner rather than later, but if that's not possible, then there's nothing you can do about that. But you don't want to panic and rush it.
Off topic but I've been on mat leave through lockdown the entire year (baby born on April 1st), so I was hoping to see my family for a quick visit before returning to work but that won't be happening now ..
I'm sorry you won't be able to see your family
.
The most important thing to focus on right now, though, is securing your immigration status and your future in the UK. Your family will still be there once you have ILR, and it's not exactly the safest time to be travelling either, so it's actually a good time to be applying for a visa.
I've just booked the test and will do as you said.
That's good
.
Just make sure you give yourself enough time to study for it, if you haven't already. I believe all the questions are taken from the study guide, so you need to know the answers that are in it. There are practice tests you can do as well.
The UKVI website links to this page for buying the study materials, though you can probably get them from Amazon or similar as well:
https://www.officiallifeintheuk.co.uk/shop