Splitting the list
Put one name on each line, then choose Number of teams or People per team. Teams come out as even as the numbers allow: ten names in three teams makes teams of 4, 3 and 3. With a team size, no team goes over it, so ten in teams of three makes 3, 3, 2 and 2. The order comes from your browser's cryptographic random source, shuffled without the small bias simpler methods have, so every split is as likely as any other.
Balancing by skill
Add a number after a name with a comma, like Alex, 3, or paste two columns from a spreadsheet. With Balance by skill on, the strongest are dealt out first, each to the team with the lowest total so far, then players are swapped between teams while a swap brings their totals closer. With no pairs to keep apart, no two teams end up further apart than the highest single number in the list. A name with no number counts as 0. Who goes where still varies each time where the numbers allow, but balanced teams change less between shuffles than random ones.
Keeping people apart
Under Keep apart, write two names a line, like Alex + Sam; a comma or & works too, and three or more names on a line are all kept apart from each other. Names match the list without regard to capitals. If there are fewer teams than people who must be kept apart, it cannot be done, and the page says which pair had to share.
Questions
Can I rename the teams?
Yes. Click a team's name and type. The names stay when you press Reshuffle, and go into the text you copy and the link.
How do I share the teams?
Copy as text gives a plain list for a group chat or an email. Copy link puts the names, the settings and the teams themselves in the page's address, so whoever opens it sees the same teams. Nothing is stored anywhere else.
Is it really random?
Without skill numbers, yes: each split that keeps your pairs apart is exactly as likely as any other. Balancing trades some randomness for even totals, since only some splits are fair on skill.
How many names can it take?
Up to 500 names and 100 teams. A very long list may be too big to fit in a link; the teams still work on the page.