general question about user agent

If i change my user agent to a random name for eg Max then will it affect the name of the client shown to the peers

in other words

Can i fake other people by showing them my client as a custom name like max

i.e. they would see my client as “max”

Most trackers, and especially private trackers, won’t accept that, so you’ll never get a peers list. The nice ones will tell you that your client is unsupported. Some trackers may permanently ban you for it.