Is it illegal to write your name or something on and underpass or abandoned building? in the uk

I see lots of tags (peoples nicknames and names) on abonded buildings and I want to start but with my nickname, but is it illegal? And if so what would the punishment be if I got caught or found out? In the Uk (scotland)
Theres alsonalot on skateparks, so it cant be illegal is it?

You can buy your own building and paint it any way you want but you can't legally tag someone else's property either public or private.

From the Scottish Police web link below:

"Graffiti in Scotland can be treated as the common law crime of malicious mischief or the statutory offence of vandalism and if prosecuted, the offender could face a fine or even imprisonment. The police can also issue fixed penalty fines for these offences.

Under 16's are not permitted to buy aerosol paint cans under the Anti-social Behaviour Scotland Act 2004."

https://www.askthe.scottish.police.uk/content/Q572.htm