I don't hand-pollinate (although I admire many of those who do). I let natural crosses happen, and work with those, and I use F2s from commercial F1s, sometimes. I've been doing that as long as I've grown tomatoes from seed (since 2014).
There are some advantages to this:
* It selects for strongly viable pollen. (For the natural crosses, I mean.)
* It selects for pollen from flowers insects find interesting, in the case of such as bee crosses.
* You don't have to do any of the crossing yourself.
* Surprises can be fun, as can the detective work / guessing about the parentage.
* Maybe it's more romantic for the tomatoes if they don't have arranged outcomes.
The downsides aren't as bad as you're probably thinking.
A really major thing I've noticed is that unremarkable F1s from natural crosses tend to have significantly more remarkable offspring. Don't let an unremarkable F1 deter you from growing the F2s. The F1 doesn't always tell you much about the desirability of the line, especially if it wasn't in good soil or some such when you grew it.
To get more crosses, I've tended to grow more varieties. I may narrow them down where I want certain groups to be more likely to cross.
I also look for sports/mutants (which can be rare, but they do happen). They can be stable right away, potentially.
With the exception of Frittata Kitchen (which is a sport of Bloody Butcher), I haven't named any varieties, yet. However, I do name my individual plants, and the resulting collection of seeds from each plant, and their names might resemble the final outcome. So, while I'm pretty sure I'm going to call a tomato Snacker when it's stable, I call the project Snacker_, and the plants such as Snacker_B, Snacker_B0, etc. (according to my naming system). The seeds of Snacker_B are called Snacker-B. For Snacker-B seeds given away, I encourage people to keep using that name as if it were the variety name (then we know which of my plants the unstable line of seeds they're growing came from). But for me, the next plants will be such as Snacker_C, Snacker_C0, Snacker_C1, etc.
I'm close to naming a Snacker_ tomato Snacker, but only because it had so many recessive traits in the F2, in 2020. This year, it was at F3, with Snacker_B being the most desirable plant. I may need to further stabilize the taste and how the calyx attaches, but otherwise, it should be stable.
It can take a long time to stabilize most crosses, though! Eight to ten+ generations is a good idea.
I name my projects at arbitary times (like when they seem to have segregated somewhat, or whenever; not at the F1, per se). So, Snacker_A was an F2 (not an F1); the F1 was very different.