Thank you for your feed back.
A potential dilemma for the future is when you leave the company.
If I find myself in your situation, I'll buy a prepaid card for the iPhone SE, and linked with your private account.
Check the conditions of a prepaid card in your region, it depends on the country.
Whoever gave the iPhone SE to you should read this this Apple article: What to do before you sell, give away, or trade in your iPhone, iPad, or iPod touch
What to do before you sell, give away, or trade in your iPhone, iPad, or iPod touch - Apple Support
Then the previous owner has to remove the iPhone from his account, see this Apple article:
Check your Apple ID device list to see where you're signed in
Check your Apple ID device list to see where you're signed in - Apple Support
Then you can sign in with your private Apple ID account.
And I will probably create new account with some fake phone number.
No . . . don't, that is not possible because you will get an error message every time you want to arrange things with Apple, such as updating iPhone, downloading app(s).
Hopefully it's clear for you, in short:
Company phone -> company email addres -> company phone number.
Private iPhone -> your private Apple ID -> prepaid card.
But it's all your choices.