How to switch to a multichannel telephone number?

Question

Telephony

The situation with telephony in our organization at the moment is as follows: there are 3 analog lines from one telephone provider, each with its own subscriber number.
I would like: office automatic telephone exchange.
What has already been done in this direction: there is an OpenVox board with a sufficient number of FXO/FXS; copper pairs brought to it from the switchboard, ready for connection at any time; server; Asterisk tuned to the current situation and the ability to slowly reconfigure it if something happens.
What suggests itself: a multi-channel number, at least for the same 3 analog lines.
What is frustrating: if you switch to a multi-line number, you have to keep one number and refuse the other two, which is undesirable from a management point of view ("some people who do not know all our numbers will not be able to get through").
Questions:
1. Is there, in principle, a service for telephone providers in which we would have all three numbers, so that these numbers are switched on the line not rigidly (1 to 1), but dynamically (when an incoming call to any of the numbers is engaged the first free line or a busy signal is issued if there are no free lines at the moment)?
2. If the service exists, what is the correct name for it?

Answer 1

And this telephone provider can't give you the same numbers via VIP?