If you can make calls and send texts, it's recognizing the TMobile network.
If you can't use the internet, you probably have the wrong APN settings in the phone. Either bring it to a TMobile store and they can set it, or go to Settings/Connections/More networks/Mobile networks/Access Point Names. Create a new access point, enter:
Name t-mobile US
apn
epx.tmobile.com
pppnumber NOTHING
proxy not set
port not set
username not set
password not set
server not set
mmsc
http://mms.msg.eng.t-mobile/mms/wapenc
multimedia message proxy not set
multimedia message port not set
service provider NOTHING
mcc310
mnc 260
authentication type not set
apn type default,supl,mms
apn protocol is auto set IPv4
turn apnon / off is auto apn turned on
bearer unspecified
mobile virtual network operator none