Re: "... I have no idea whether it’s a business call or a personal call, because there is visible one label (of the eSIM) ..."
Answer:
The incoming lines are identified by the small "box" indicator with a single letter in it - displayed immediately ahead of the CallerID. - .
The letter displayed in the box is simply the first letter of the "name" you've assigned to the line in Settings-> Mobile[Cellular]
(e.g. P=Primary, A=Alternate, A=AT&T, V=Verizon, W=Work, P=Personal, S=Secondary, ... etc.)
This "identifier" is displayed on the incoming call "pop up" and is also displayed in the call logs.
Commentary:
IMO, this is one area presenting Apple w/ an "opportunity for product improvement."
Visual Indication -- The incoming lines could be have more distinctive indication (e.g. Color vice the small B&W box w/ a single letter letter)
Audible Indication -- Clearly the ability to set a different ringtone for each line would ba a HUGE benefit.
Desired improvements aside ... once you become accustomed to looking for the "Indicator Box" in addition to the incoming CallerID ... it's certainly "functional" even if not [yet] everything we might like to have.
See also: Using Dual SIM with an eSIM - Apple Support
Suggest you might provide product feedback re: this to: Feedback - iPhone - Apple