There are various ways you could say it:

Spike is ainm do mo mhadadh

Spike an t-ainm atá ar mo mhadadh

Is é Spike ainm mo mhadaidh

"Madra" and "madadh", by the way, are just the words for dog in different dialects. I use "madadh" since I speak Ulster Irish, but you could use "madra" just as well in the above sentences.