Are planes assigned different climb angles from the airport by the tower? Clearly the angle at which planes take off and climb depends on lots of things (mountains, residential area, aircraft type, wind) but when watching planes take off after another from the same runway, I have the impression that similar aircraft climb at different angles right after another.

So I'm wondering it this is a measure to increase the distance between two planes quickly after they leave the airport? Such that every other aircraft is asked to leave flat'ish (within what the plane and regulations allow) and others more steeply?

The question occurred to me at GVA (single commercial runway).

This is about the initial climb angle, not their course heading.
There can be many reasons. Flights taking off one after another:


have different destinations
have different weight and balance
have difference in wings and wingtips
have pilots with difference in skills
got different takeoff directions by ATC
are trying to avoid wake turbulence


Off all the reasons I mentioned above, perhaps wake turbulence might be playing more role about difference in takeoff angle. There are a ton of questions about wake turbulence, which is worth a read.