thats is running now, and returns a lot of text on the serial monitor
Nothing happens automatically. You must have some code that makes this happen. Where is that code?
now i have the name that i want to return on the display between tags
OK.
but the server sends me
A bunch of stuff that includes the stuff of interest.
Perhaps you noticed that blank line, there. The data of interest follows that blank line. So, read and discard (or display on the serial monitor) the characters up to the empty line. You'll need to determine whether the blank line is caused by '\n', '\r', '\n', '\r' or by '\r', '\n', '\r', '\n' or by '\n', '\n', or by '\r', '\r'. It will be one of those 4 sets of characters that precedes the data of interest.
Of course, since you are sending a character to mark the start of your data ('<'), you could just read and discard data until that arrives. Then, read and discard data until the '>' arrives. Then, read and store data until the next '<' arrives. Then, read and discard data until the client runs out of data.
Then, show the stored data on the LCD.