Telling your altitude/level upon calling ATC initially, is for them to compare your report with their readout.
That is since... 40 years ago, and my explanation dates from the same era...
xxx
Nowadays, when tower would transfer me to departure frequency, my call would be -
"Departure, flight XXX out of two thousand climbing to fife zero, good evening"...
That tells them I am vacating 2000 ft, and that they can clear other plane to that altitude.
And it implies that I request higher level... and a more direct routing if available.
These ATC guys know all that. They are "pros" as well.
As simple as that.
xxx
Happy contrails