Should I name my web app to my firstname

Depends on what it is you're doing. If it's a small personal project, sure. If it's something you're trying to market as serious software, your first name won't look very professional.

The good thing about software is it's easy enough to rename. So you can name it alexlab today, and then a year from now, rebrand it to Lab Co or something else.

You could use your initials, like ggml. Makes it less cutesy (not quite the right word) but still open up the domain name space

I used to do this. It became a problem when it goes pro. One product was acquired and the acquirer would edit out the package name in screenshots.

Unless you can fit your name into a pun in some way like Automattic or Page Rank.

xelab or balex

I think it's better to tack on an extra (related) word like how movies add "movie" to their domain name.

One common trick for software is to add "get" or "join" to the beginning like:

- https://www.getdropbox.com/

- https://www.joinhoney.com/

A longer, targeted domain name could actually perform better if you understand the niche you are targeting. (And it's usually better to target a niche.) Can't think of any super examples off the top of my head, but something like:

- https://www.unlockyourhipflexors.com/